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Bibliographic Details
Main Author: Du, Chengyu
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2405.03216
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Table of Contents:
  • The modules $A_\mathfrak{q}(λ)$ of $U(p,q)$ can be parameterized by their annihilators and asymptotic supports, both of which can be identified using Young tableaux. Trapa developed an algorithm for determining the tableaux of the modules $A_\mathfrak{q}(λ)$ in the mediocre range, along with an equivalent condition to determine non-vanishing. The condition involves a combinatorial concept called the overlap, which is not straightforward to compute. In this paper, we establish a formula for the overlap and simplify the condition for ease of use. We then apply it to $K$-types and the Dirac index of $A_\mathfrak{q}(λ)$.