Pith Number

pith:G5P4ABSH

pith:2026:G5P4ABSHARUO7X72XBTZ7VPE2V

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Complex Weyl correspondence and harmonic representation of $SU(p,q)$

Benjamin Cahen

The paper gives explicit formulas for the complex Weyl symbols of the harmonic representation operators of SU(p,q) on the Fock space.

arxiv:2605.15296 v1 · 2026-05-14 · math.RT

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\pithnumber{G5P4ABSHARUO7X72XBTZ7VPE2V}

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4 Citations open

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Claims

C1strongest claim

We give explicit formulas for the complex Weyl symbols of the harmonic representation operators.

C2weakest assumption

The harmonic representation of SU(p,q) is realized on the Fock space in a manner compatible with the complex Weyl correspondence.

C3one line summary

Explicit formulas are given for the complex Weyl symbols of the harmonic representation operators of SU(p,q) and its extension by the (2p+2q+1)-dimensional Heisenberg group.

References

30 extracted · 30 resolved · 0 Pith anchors

[1] J. Arazy and H. Upmeier, Invariant symbolic calculi and eigenvalues of invariant operators on sym- metric domains , Function spaces, interpolation theory and related topics (Lund, 2000) 151-211, de Gr 2000

[2] J. Arazy and H. Upmeier, Weyl Calculus for Complex and Real Symmetric Domains , Harmonic analysis on complex homogeneous domains and Lie groups (Rome, 2001). Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. 2001

[3] F. A. Berezin, Quantization, Math. USSR Izv. 8, 5 (1974), 1109-1165 1974

[4] F. A. Berezin, Quantization in complex symmetric domains, Math. USSR Izv. 9, 2 (1975), 341-379 1975

[5] R. J. Blattner and J. H. Rawnsley, Quantization of the action of U(k, l ) on R2(k+l), J. Funct. Anal. 50 (1983), 188–214 1983

Receipt and verification

First computed	2026-05-20T00:00:51.199519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

375fc006470468efdffab8679fd5e4d5605adcf82d37c01543d7e86f274d2b08

Aliases

arxiv: 2605.15296 · arxiv_version: 2605.15296v1 · doi: 10.48550/arxiv.2605.15296 · pith_short_12: G5P4ABSHARUO · pith_short_16: G5P4ABSHARUO7X72 · pith_short_8: G5P4ABSH

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/G5P4ABSHARUO7X72XBTZ7VPE2V \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 375fc006470468efdffab8679fd5e4d5605adcf82d37c01543d7e86f274d2b08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0690b0a45faf1a9220b3037a3fb5ff62c14cf28525791f360d50ca94dee72ac2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-05-14T18:11:02Z",
    "title_canon_sha256": "f304d98ae794b168c1f164221462108033f75c0d90eff8d02be2497c6e7fbd1b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15296",
    "kind": "arxiv",
    "version": 1
  }
}