Method of quantum characters in equivariant quantization

A. Mudrov; J. Donin

RECORD

Method of quantum characters in equivariant quantization

J. Donin, A. Mudrov

Quantum Algebra · Submitted 24 Apr 2002

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

The authors' main claim It turns out that they are in one-to-one correspondence with characters of the algebra $\A_h(M)$.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,413 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Let $G$ be a reductive Lie group, $\g$ its Lie algebra, and $M$ a $G$-manifold. Suppose $\A_h(M)$ is a $\U_h(\g)$-equivariant quantization of the function algebra $\A(M)$ on $M$. We develop a method of building $\U_h(\g)$-equivariant quantization on $G$-orbits in $M$ as quotients of $\A_h(M)$. We are concerned with those quantizations that may be simultaneously represented as subalgebras in $\U^*_h(\g)$ and quotients of $\A_h(M)$. It turns out that they are in one-to-one correspondence with characters of the algebra $\A_h(M)$. We specialize our approach to the situation $\g=gl(n,\C)$, $M=\End(\C^n)$, and $\A_h(M)$ the so-called reflection equation algebra associated with the representation of $\U_h(\g)$ on $\C^n$. For this particular case, we present in an explicit form all possible quantizations of this type; they cover symmetric and bisymmetric orbits. We build a two-parameter deformation family and obtain, as a limit case, the $\U(\g)$-equivariant quantization of the Kirillov-Kostant-Souriau bracket on symmetric orbits.

background contribution method result interpretation main claim

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	Let $G$ be a reductive Lie group, $\g$ its Lie algebra, and $M$ a $G$-manifold.	background 1.00	0.06	0.02	asserted 0.70
s1	Suppose $\A_h(M)$ is a $\U_h(\g)$-equivariant quantization of the function algebra $\A(M)$ on $M$.	background 1.00	0.08	0.02	asserted 0.83
s2	We develop a method of building $\U_h(\g)$-equivariant quantization on $G$-orbits in $M$ as quotients of $\A_h(M)$.	contribution 0.60	0.94	0.20	asserted 1.00
s3	We are concerned with those quantizations that may be simultaneously represented as subalgebras in $\U^*_h(\g)$ and quotients of $\A_h(M)$.	contribution 0.74	0.37	0.09	hedged possibility 0.75
s4	It turns out that they are in one-to-one correspondence with characters of the algebra $\A_h(M)$.	result 0.98	0.84	0.52	asserted 1.00
s5	We specialize our approach to the situation $\g=gl(n,\C)$, $M=\End(\C^n)$, and $\A_h(M)$ the so-called reflection equation algebra associated with the representation of $\U_h(\g)$ on $\C^n$.	contribution 0.67	0.64	0.05	asserted 0.97
s6	For this particular case, we present in an explicit form all possible quantizations of this type; they cover symmetric and bisymmetric orbits.	result 0.75	0.94	0.17	asserted 1.00
s7	We build a two-parameter deformation family and obtain, as a limit case, the $\U(\g)$-equivariant quantization of the Kirillov-Kostant-Souriau bracket on symmetric orbits.	result 0.81	0.95	0.21	asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.96 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Let $G$ be a reductive Lie group, $\g$ its Lie algebra, and $M$ a $G$-manifold. Suppose $\A_h(M)$ is a $\U_h(\g)$-equivariant quantization of the function algebra $\A(M)$ on $M$. We develop a method of building $\U_h(\g)$-equivariant quantization on $G$-orbits in $M$ as quotients of $\A_h(M)$. We are concerned with those quantizations that may be simultaneously represented as subalgebras in $\U^*_h(\g)$ and quotients of $\A_h(M)$. It turns out that they are in one-to-one correspondence with characters of the algebra $\A_h(M)$. We specialize our approach to the situation $\g=gl(n,\C)$, $M=\End(\C^n)$, and $\A_h(M)$ the so-called reflection equation algebra associated with the representation of $\U_h(\g)$ on $\C^n$. For this particular case, we present in an explicit form all possible quantizations of this type; they cover symmetric and bisymmetric orbits. We build a two-parameter deformation family and obtain, as a limit case, the $\U(\g)$-equivariant quantization of the Kirillov-Kostant-Souriau bracket on symmetric orbits.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.