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Mathematics > Representation Theory
Title: Irreducible components in Hochschild cohomology of flag varieties
(Submitted on 16 Apr 2024 (v1), last revised 22 Apr 2024 (this version, v2))
Abstract: Let $G$ be a simple, simply-connected complex algebraic group with Lie algebra $\mathfrak{g}$, and $G/B$ the associated complete flag variety. The Hochschild cohomology $HH^\bullet(G/B)$ is a geometric invariant of the flag variety related to its generalized deformation theory and has the structure of a $\mathfrak{g}$-module. We study this invariant via representation-theoretic methods; in particular, we give a complete list of irreducible subrepresentations in $HH^\bullet(G/B)$ when $G=SL_n(\mathbb{C})$ or is of exceptional type (and conjecturally for all types) along with nontrivial lower bounds on their multiplicities. These results follow from a conjecture due to Kostant on the structure of the tensor product representation $V(\rho) \otimes V(\rho)$.
Submission history
From: Sam Jeralds [view email][v1] Tue, 16 Apr 2024 03:37:25 GMT (14kb)
[v2] Mon, 22 Apr 2024 06:50:52 GMT (15kb)
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