Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Branching algebras for the general linear Lie superalgebra (2403.11393v1)

Published 18 Mar 2024 in math.RT, math-ph, and math.MP

Abstract: We develop an algebraic approach to the branching of representations of the general linear Lie superalgebra $\mathfrak{gl}{p|q}({\mathbb C})$, by constructing certain super commutative algebras whose structure encodes the branching rules. Using this approach, we derive the branching rules for restricting any irreducible polynomial representation $V$ of $\mathfrak{gl}{p|q}({\mathbb C})$ to a regular subalgebra isomorphic to $\mathfrak{gl}{r|s}({\mathbb C})\oplus \mathfrak{gl}{r'|s'}({\mathbb C})$, $\mathfrak{gl}{r|s}({\mathbb C})\oplus\mathfrak{gl}_1({\mathbb C}){r'+s'}$ or $\mathfrak{gl}{r|s}({\mathbb C})$, with $r+r'=p$ and $s+s'=q$. In the case of $\mathfrak{gl}{r|s}({\mathbb C})\oplus\mathfrak{gl}_1({\mathbb C}){r'+s'}$ with $s=0$ or $s=1$ but general $r$, we also construct a basis for the space of $\mathfrak{gl}{r|s}({\mathbb C})$ highest weight vectors in $V$; when $r=s=0$, the branching rule leads to explicit expressions for the weight multiplicities of $V$ in terms of Kostka numbers.

Citations (1)

Summary

We haven't generated a summary for this paper yet.

X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets