arXiv subjects

Aparna Upadhyay

Publications and source records attributed to Aparna Upadhyay.

4 recordsLinked to original sources

arXiv2026

Classification of Collisions of Twisted Foulkes Character Polynomials

The twisted Foulkes character polynomial is an algebraically defined polynomial attached to an integer partition. We determine precisely how much combinatorial information this polynomial encodes by completely classifying all pairs of partitions that give rise to the same polynomial. Our main result shows that equality of twisted Foulkes character polynomials admits a purely combinatorial characterization in terms of two explicit local operations on partitions.

math.CO↗

arXiv2021

Recursive sequences attached to modular representations of finite groups

The core of a finite-dimensional modular representation $M$ of a finite group $G$ is its largest non-projective summand. We prove that the dimensions of the cores of $M^{\otimes n}$ have algebraic Hilbert series when $M$ is Omega-algebraic, in the sense that the non-projective summands of $M^{\otimes n}$ fall into finitely many orbits under the action of the syzygy operator $Ω$. Similarly, we prove that these dimension sequences are eventually linearly recursive when $M$ is what we term $Ω^{+}$-algebraic. This partially answers a conjecture by Benson and Symonds. Along the way, we also prove a number of auxiliary permanence results for linear recurrence under operations on multi-variable sequences.

math.RT↗

arXiv2021

The Benson -- Symonds Invariant for Ordinary and Signed Permutation Modules

The signed permutation modules are a simultaneous generalization of the ordinary permutation modules and the twisted permutation modules of the symmetric group. In a recent paper Dave Benson and Peter Symonds defined a new invariant $γ_G(M)$ for a finite dimensional module $M$ of a finite group $G$ which attempts to quantify how close a module is to being projective. In this paper, we determine this invariant for all the signed permutation modules of the symmetric group using tools from representation theory and combinatorics.

math.RT↗

arXiv2020

The Benson-Symonds Invariant for Permutation Modules

In a recent paper, Dave Benson and Peter Symonds defined a new invariant $γ_G(M)$ for a finite dimensional module $M$ of a finite group $G$ which attempts to quantify how close a module is to being projective. In this paper, we determine this invariant for permutation modules of the symmetric group corresponding to two-part partitions using tools from representation theory and combinatorics.

math.RT↗