A Note on Group Representations, Determinantal Hypersurfaces and Their Quantizations

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt

Standard

A Note on Group Representations, Determinantal Hypersurfaces and Their Quantizations. / Klep, I.; Volčič, J.

Operator Theory, Functional Analysis and Application. Springer, 2021. s. 393-402.

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt

Harvard

Klep, I & Volčič, J 2021, A Note on Group Representations, Determinantal Hypersurfaces and Their Quantizations. i Operator Theory, Functional Analysis and Application. Springer, s. 393-402. https://doi.org/10.1007/978-3-030-51945-2_19

APA

Klep, I., & Volčič, J. (2021). A Note on Group Representations, Determinantal Hypersurfaces and Their Quantizations. I Operator Theory, Functional Analysis and Application (s. 393-402). Springer. https://doi.org/10.1007/978-3-030-51945-2_19

Vancouver

Klep I, Volčič J. A Note on Group Representations, Determinantal Hypersurfaces and Their Quantizations. I Operator Theory, Functional Analysis and Application. Springer. 2021. s. 393-402 https://doi.org/10.1007/978-3-030-51945-2_19

Author

Klep, I. ; Volčič, J. / A Note on Group Representations, Determinantal Hypersurfaces and Their Quantizations. Operator Theory, Functional Analysis and Application. Springer, 2021. s. 393-402

Bibtex

@inproceedings{d291dc0511cd4cbd90825eaa8194a101,
title = "A Note on Group Representations, Determinantal Hypersurfaces and Their Quantizations",
abstract = "Recently, there have been exciting developments on the interplay between representation theory of finite groups and determinantal hypersurfaces. For example, a finite Coxeter group is determined by the determinantal hypersurface described by its natural generators under the regular representation. This short note solves three problems about extending this result in the negative. On the affirmative side, it is shown that a quantization of a determinantal hypersurface, the so-called free locus, correlates well with representation theory. If A1,…,Aℓ∈GLd(C) generate a finite group G, then the family of hypersurfaces {X∈Mn(C)d:det(I+A1⊗X1+⋯+Aℓ⊗Xℓ)=0} for n∈N determines G up to isomorphism.",
author = "I. Klep and J. Vol{\v c}i{\v c}",
year = "2021",
doi = "10.1007/978-3-030-51945-2_19",
language = "English",
pages = "393--402",
booktitle = "Operator Theory, Functional Analysis and Application",
publisher = "Springer",
address = "Switzerland",

}

RIS

TY - GEN

T1 - A Note on Group Representations, Determinantal Hypersurfaces and Their Quantizations

AU - Klep, I.

AU - Volčič, J.

PY - 2021

Y1 - 2021

N2 - Recently, there have been exciting developments on the interplay between representation theory of finite groups and determinantal hypersurfaces. For example, a finite Coxeter group is determined by the determinantal hypersurface described by its natural generators under the regular representation. This short note solves three problems about extending this result in the negative. On the affirmative side, it is shown that a quantization of a determinantal hypersurface, the so-called free locus, correlates well with representation theory. If A1,…,Aℓ∈GLd(C) generate a finite group G, then the family of hypersurfaces {X∈Mn(C)d:det(I+A1⊗X1+⋯+Aℓ⊗Xℓ)=0} for n∈N determines G up to isomorphism.

AB - Recently, there have been exciting developments on the interplay between representation theory of finite groups and determinantal hypersurfaces. For example, a finite Coxeter group is determined by the determinantal hypersurface described by its natural generators under the regular representation. This short note solves three problems about extending this result in the negative. On the affirmative side, it is shown that a quantization of a determinantal hypersurface, the so-called free locus, correlates well with representation theory. If A1,…,Aℓ∈GLd(C) generate a finite group G, then the family of hypersurfaces {X∈Mn(C)d:det(I+A1⊗X1+⋯+Aℓ⊗Xℓ)=0} for n∈N determines G up to isomorphism.

UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85103662329&partnerID=MN8TOARS

U2 - 10.1007/978-3-030-51945-2_19

DO - 10.1007/978-3-030-51945-2_19

M3 - Article in proceedings

SP - 393

EP - 402

BT - Operator Theory, Functional Analysis and Application

PB - Springer

ER -

ID: 297045016