William Q. Erickson

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20232026

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6 papers · 1 filter

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.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…