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Paper Citation Record · LEDGER

Computing the real Weyl group

As of 4 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:1907.01398.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
1907.01398 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-25T10:28:10.745487Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-03T06:30:56.289259+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

26 of 26 outbound references displayed

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  • verified fuzzy16
  • unresolved8
  • parse uncertain0
  • malformed identifier2
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d8037f8b-5dbc-4600-93b3-9b7c65ae0bff · outbound

This paper cites /T_he adjoint gr oup Gc of gc is the identity component (in the Zariski topology) of the automorph ism group of gc.

Computing the real Weyl group /T_he adjoint gr oup Gc of gc is the identity component (in the Zariski topology) of the automorph ism group of gc

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T10:30:39.647284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:bd7ae28d456b0f984862fa214c5373a1ca57547c156217ec6037bb57c3974925

Observation 91e681e8-c33d-4d05-88ff-4ba2153924a3 · outbound

This paper cites /T_hroughout, we use the following notation.

Computing the real Weyl group /T_hroughout, we use the following notation

Reference 2

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raw_fallback, observed 2026-05-25T10:30:39.681976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:d2178a5b46afe9cfb9711f0bc911954dfecaf0e1700d73b895425ec7b14e992c

Observation 494f4015-e69f-4e2d-aaed-be73575c6853 · outbound

This paper cites Let Ψ be a root system and recall that we write W (Ψ) for its Weyl group.

Computing the real Weyl group Let Ψ be a root system and recall that we write W (Ψ) for its Weyl group

Reference 3

Resolution
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raw_fallback, observed 2026-05-25T10:30:39.705768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:23f465654549a546d0b46f6fce354304831115af403e9a3e55ce5e89eced3340

Observation 473c5843-af21-4198-bf3b-31b5d828edcd · outbound

This paper cites As a preliminary step, in the next lemma we recall the following facts from [12, Lemmas 5.1.4 & 5.2.22] and [6, Lemma 6.1].

Computing the real Weyl group As a preliminary step, in the next lemma we recall the following facts from [12, Lemmas 5.1.4 & 5.2.22] and [6, Lemma 6.1]

Reference 4

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raw_fallback, observed 2026-05-25T10:30:39.643378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:d5b794aa91e81158e1c044badae234cdad22340cfa93037ee4da6c7937489d85

Observation b137bcfe-d0f3-451b-8301-0c75f636b4a3 · outbound

This paper cites (4) N ˜G( ˜H c(R)) = N ˜G(h): Using (3), we see that g ∈ ˜G normalises ˜H c(R) if and only if it normalises ˜H c, if and only if it normalises hc, if and only if it normalises h.

Computing the real Weyl group (4) N ˜G( ˜H c(R)) = N ˜G(h): Using (3), we see that g ∈ ˜G normalises ˜H c(R) if and only if it normalises ˜H c, if and only if it normalises hc, if and only if it normalises h

Reference 5

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:5454bf3f227bc0eda77b4077188bd53d42dd2f27ef7b15d4c8ca23fd330d7f71

Observation 6bbce283-6160-4932-bb69-42929d8f720e · outbound

This paper cites Based on the description provided here, the implementation of all steps of the algorithm is straightforwar d so we will not comment on this.

Computing the real Weyl group Based on the description provided here, the implementation of all steps of the algorithm is straightforwar d so we will not comment on this

Reference 6

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:487c7e5fe58b594e0513e7d7810ebccbfbf9170cd22ddbbf93145a426e502c9e

Observation f4337c1d-3f7e-4a0c-9ec5-f8415c869c8f · outbound

This paper cites See liegroups.org.

Computing the real Weyl group See liegroups.org

Reference 7

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source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:b2827974f8565dff94ba8c2f2c9ad6b4485c8c36ec57f748a8d2e6562e73ea17

Observation c1093119-3c64-4ce9-b4e0-87fdad759169 · outbound

This paper cites Adams and F.

Computing the real Weyl group Adams and F

Reference 8

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source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:23867bdd22bc33e452fac57c0a7ce3d20d5589c1ad1b811ae423cace9608f16c

Observation de56a073-1f12-44f6-b148-740af57b798e · outbound

This paper cites Adams and O.

Computing the real Weyl group Adams and O

Reference 9

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source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:8204bcb91603c6610b918237d0e6ed590c4a5e3493eea8f13e6b06d5f01983d4

Observation 2f1f1a6e-69f1-42ad-abd1-135ae155442d · outbound

This paper cites an unresolved cited work.

Computing the real Weyl group Unresolved cited work

Reference 10

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source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:3c56cb4ffeb8b54b3717cee5c68ffd73da52e9eced467aef021331aa3a378994

Observation 063c1c6c-11c4-47dc-b89f-8edefb864bd3 · outbound

This paper cites Chevalley.

Computing the real Weyl group Chevalley

Reference 11

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source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:e1530d97f3a752cb0378d6351b6636058a0ab4adc4fd28d27ae27b94c3851d8c

Observation c95785dd-c540-4dce-9b92-06f9423e721d · outbound

This paper cites Dietrich, P.

Computing the real Weyl group Dietrich, P

Reference 12

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No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:6cfe59e18d02f989a29136221271f4aa914dd268f05394bdf1c55110f111cffe

Observation 05143ef0-2d9c-4bcc-92a4-94b7ea015950 · outbound

This paper cites Dietrich, P.

Computing the real Weyl group Dietrich, P

Reference 13

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No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:983e9f68085a550aa5f759e0c82b9fb094827c1e0272134c0bf6e409ed3ba468

Observation 7b4ed286-ffde-4a7a-879f-3684d8e2a894 · outbound

This paper cites Dietrich, W.

Computing the real Weyl group Dietrich, W

Reference 14

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No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:93c24acd74251d2067a7843c5ebc5291252252b0237d35c5185773e7a24a8735

Observation ab5078db-962b-44b7-80bf-3368bea4e016 · outbound

This paper cites GAP – groups, algorithms, and programming.

Computing the real Weyl group GAP – groups, algorithms, and programming

Reference 15

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No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:daf074fdfd8250bf7702446e05a67469f00c8f9900fa7c7c5a84b0692fe95191

Observation 66b95a8a-635e-4e74-9696-36746d81d9f4 · outbound

This paper cites du Cloux.

Computing the real Weyl group du Cloux

Reference 16

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No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:57cc6279a11e28d4c78e55307398ae1d6b1061ce838794a6d287657fb2c899a3

Observation 9ce447ed-1715-4f2d-af04-cb92f634a9b5 · outbound

This paper cites an unresolved cited work.

Computing the real Weyl group Unresolved cited work

Reference 17

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No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:a1c5ecc9dc2e1a19ec43873cdcc1b813428845d17ba99fec5582be3705b6e75c

Observation f525abca-506c-4dea-9874-71f9d38f30e6 · outbound

This paper cites an unresolved cited work.

Computing the real Weyl group Unresolved cited work

Reference 18

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No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:abdc77498eebc372e70cf46fbe30f197dc6c2e7d15f67da93110fe194fe28fb7

Observation 096cc75d-bd3e-4ffe-bdce-181f2c2207b0 · outbound

This paper cites an unresolved cited work.

Computing the real Weyl group Unresolved cited work

Reference 19

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No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:85728cb1991a9e43cedbf2566671c1100dada129558f5cd5524869058f4c29e1

Observation bca8bd87-4d9a-44f7-b0e3-6f55fddeb4d6 · outbound

This paper cites Helgason.

Computing the real Weyl group Helgason

Reference 20

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source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:05d57e6e5ae8d28442d38ea2ce14589d8ca2e4a4697216ed636ce32c8afd7d28

Observation 17d5c833-eca3-4979-86a5-58ca0985613d · outbound

This paper cites an unresolved cited work.

Computing the real Weyl group Unresolved cited work

Reference 21

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source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:b9d4d94f2ec997d2ce0f94668cb1a3fc930689be91e90537d6462488f3306ed3

Observation 947af2be-623b-47e0-8671-88762b88fa49 · outbound

This paper cites an unresolved cited work.

Computing the real Weyl group Unresolved cited work

Reference 22

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No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:97e3b92975bb346c401de759fc0fd380ff348d0a4731f9eceaf242ed237fbe21

Observation 0ff56ae1-216a-47b1-8659-e3781a4c3a31 · outbound

This paper cites an unresolved cited work.

Computing the real Weyl group Unresolved cited work

Reference 23

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No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:34999023d31fb6e04eecddac78a3c7bbce3188b020a969ce27e9b0cf7877f1f1

Observation b4ca5be5-9be7-40d4-b569-b685996294ef · outbound

This paper cites Onishchik.

Computing the real Weyl group Onishchik

Reference 24

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No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:28ea4145bba6995f426844217ffb5edd2156686bf1ab5331260a695828612b0c

Observation 5d770b06-24c1-4878-9f6d-83b5ba20b5d6 · outbound

This paper cites Steinberg.

Computing the real Weyl group Steinberg

Reference 25

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No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:68a9556186d9d16645c5bafd1c8b0defcc8a8c576c97ef2cfab1c8d00b984af5

Observation b350427c-2946-4fba-a185-ae5b52e24d51 · outbound

This paper cites an unresolved cited work.

Computing the real Weyl group Unresolved cited work

Reference 26

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raw_fallback, observed 2026-05-25T10:30:39.658415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-05-25T10:28:10.745487Z digest=sha256:39ac802f6312ed4367e19fc00fe5f4e66b70203886255b1b66af396ab20d8130

Pith citing papers

No inbound Pith citation observations are available.