The canonical basis of the quantum adjoint representation

G. Lusztig

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The canonical basis of the quantum adjoint representation

G. Lusztig

Representation Theory · Submitted 23 Feb 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We identify the canonical basis of the quantum adjoint representation of a quantized enveloping algebra with a basis that we defined before the theory of canonical bases was available.

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What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.77 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We identify the canonical basis of the quantum adjoint representation of a quantized enveloping algebra with a basis that we defined before the theory of canonical bases was available.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We identify the canonical basis of the quantum adjoint representation of a quantized enveloping algebra with a basis that we defined before the theory of canonical bases was available.	result 0.65	0.85	0.86	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.94.

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The paper

Original abstract

We identify the canonical basis of the quantum adjoint representation of a quantized enveloping algebra with a basis that we defined before the theory of canonical bases was available.

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3 arXiv papers cite this in 6 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 4 sentences without a confident label

Uses its method or tool 2 papers

Following Lusztig [ref] , [ref] , we obtain the Chevalley groups corresponding to $⊆(M)$ as follows.

On the construction of semisimple Lie algebras and Chevalley groups · The Lie algebra generated by $e_i,f_i$ · 0.96
Starting from $R ⊂^8$, one can write down a basis and multiplication table for the Lie algebra $_8$ over $$ as in [ref] or [ref] .

$E_8$, the most exceptional group · From the root system to the Lie algebra · 0.81

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