William Q. Erickson

activity

20232026

collaborators

8 papers

math.CO2026

Explicit marginal distributions for permutations with prescribed Robinson-Schensted shape

William Q. Erickson

Given a permutation $σ$ , the Robinson-Schensted correspondence determines a certain partition called the shape of $σ$ . Famously, the shape measures the longest unions of increasing…

math.RT2025

Unitarity of highest weight Harish-Chandra modules and smoothness of Schubert varieties

Zhanqiang Bai, William Q. Erickson, Markus Hunziker +1

Let $G_{R}$ be a Lie group of Hermitian type, and $L (λ)$ a highest weight Harish-Chandra module of $G_{R}$ with highest weight $λ$ . In this article, we exhibit a…

math.RT2025

$K$ -type multiplicities in degenerate principal series via Howe duality

Mark Colarusso, William Q. Erickson, Andrew Frohmader +1

Let $K$ be one of the complex classical groups $O_{k}$ , $GL_{k}$ , or $Sp_{2 k}$ . Let $M \subseteq K$ be the block diagonal embedding ${\rm O}_{k_1} \times \cdots \time…

math.CO2024

Robinson-Schensted shapes arising from cycle decompositions

Martha Du Preez, William Q. Erickson, Jonathan Feigert +5

In the symmetric group $S_{n}$ , each element $σ$ has an associated cycle type $α$ , a partition of $n$ that identifies the conjugacy class of $σ$ . The Robinson-Schensted (RS) correspo…

math.CO2024

A combinatorial interpretation of the Bernstein degree of unitary highest weight modules

William Q. Erickson, Markus Hunziker

The Bernstein degree ( $Deg$ ) is a fundamental invariant of admissible representations of a real reductive Lie group $G_{R}$ . Our main result concerns the cl…

math.CO2024

Tensor invariants for classical groups revisited

William Q. Erickson, Markus Hunziker

We reconsider an old problem, namely the dimension of the $G$ -invariant subspace in $V^{\otimes p} \otimes V^{*\otimes q}$ , where $G$ is one of the classical groups $GL (V)$ ,…

math.CO2023

Stanley decompositions of modules of covariants

William Q. Erickson, Markus Hunziker

Let $H$ be a complex reductive group, with finite-dimensional representations $W$ and $U$ . The module of covariants for $W$ of type $U$ is the space of all $H$ -equivariant polynomi…

math.CO2023

Stanley decompositions of rings of invariants and certain highest weight Harish-Chandra modules

William Q. Erickson, Markus Hunziker

The first half of this paper is largely expository, wherein we present a systematic combinatorial approach to the theory of polynomial (semi)invariants and multilinear invariants o…

Explicit marginal distributions for permutations with prescribed Robinson-Schensted shape

Unitarity of highest weight Harish-Chandra modules and smoothness of Schubert varieties

K-type multiplicities in degenerate principal series via Howe duality

Robinson-Schensted shapes arising from cycle decompositions

A combinatorial interpretation of the Bernstein degree of unitary highest weight modules

Tensor invariants for classical groups revisited

Stanley decompositions of modules of covariants

Stanley decompositions of rings of invariants and certain highest weight Harish-Chandra modules

$K$ -type multiplicities in degenerate principal series via Howe duality