The Extension groups of one $\rm K$-type representations of graded Hecke algebra
Year: 2026
Type: preprint
Abstract: We study the extension groups between one $\rm K$-type representations of the graded Hecke algebra $\mathbb H$. A one $\rm K$-type representation is a Hermitian representation of $\mbb H$ whose restriction to the Weyl group is irreducible. Using a Koszul-type resolution of $\mathbb H$-modules, we reduce the computation of $\operatorname{Ext}_{\mathbb H}^j(X,Y)$ to a combinatorial count, yielding explicit formulas for the classical types and a computer computation for the exceptional types.
Source: arXiv (Cornell University)
Author: Chen, Quanyong
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225261051
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