A Hecke-equivariant decomposition of spaces of Drinfeld cusp forms via representation theory, and an investigation of its subfactors [PDF]
Research in Number Theory, 2021 There are various reasons why a naive analog of the Maeda conjecture has to fail for Drinfeld cusp forms. Focussing on double cusp forms and using the link found by Teitelbaum between Drinfeld cusp forms and certain harmonic cochains, we observed a while
Gebhard Boeckle +2 more
semanticscholar +1 more source
On the geometry and representation theory of isomeric matrices [PDF]
Algebra & Number Theory, 2021 . The space of n × m complex matrices can be regarded as an algebraic variety on which the group GL n × GL m acts. There is a rich interaction between geometry and representation theory in this example.
Rohit Nagpal +2 more
semanticscholar +1 more source
Extension of Whittaker functions and test vectors [PDF]
Research in Number Theory, 2017 We show that certain products of Whittaker functions and Schwartz functions on a general linear group extend to Whittaker functions on a larger general linear group. This generalizes results of Cogdell and Piatetski-Shapiro (Representation Theory, Number
R. Kurinczuk, N. Matringe
semanticscholar +2 more sources
Poly-analytic Functions and Representation Theory [PDF]
Complex Analysis and Operator Theory, 2021 We propose the Lie-algebraic interpretation of poly-analytic functions in L2(C,dμ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage ...
A. Turbiner, N. Vasilevski
semanticscholar +1 more source
Coxeter combinatorics for sum formulas in the representation theory of algebraic groups [PDF]
Representation Theory: An Electronic Journal of the AMS, 2021 Let G G be a simple algebraic group over an algebraically closed field F \mathbb {F} of characteristic p ≥ h p \geq h , the Coxeter number of G G .
J. Gruber
semanticscholar +1 more source
Connecting Proof Theory and Knowledge Representation: Sequent Calculi and the Chase with Existential Rules [PDF]
International Conference on Principles of Knowledge Representation and Reasoning, 2023 Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology.
Tim S. Lyon, Piotr Ostropolski-Nalewaja
semanticscholar +1 more source
On modular Harish-Chandra series of finite unitary groups [PDF]
Representation Theory: An Electronic Journal of the AMS, 2019 In the modular representation theory of finite unitary groups when the characteristic ℓ \ell of the ground field is a unitary prime, the s l ^
E. Norton
semanticscholar +1 more source
Content systems and deformations of cyclotomic KLR algebras of type
Annals of Representation Theory, 2022 This paper initiates a systematic study of the cyclotomic KLR algebras of affine types $A$ and $C$. We start by introducing a graded deformation of these algebras and the constructing all of the irreducible representations of the deformed cyclotomic KLR ...
A. Evseev, Andrew Mathas
semanticscholar +1 more source
Representation theory of vertex operator algebras and orbifold conformal field theory [PDF]
Lie Groups, Number Theory, and Vertex
Algebras, 2020 We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a program to construct conformal field theories.
Yi-Zhi Huang
semanticscholar +1 more source
The semi-linear representation theory of the infinite symmetric group [PDF]
Representation Theory: An Electronic Journal of the AMS, 2019 We study the category A \mathcal {A} of smooth semilinear representations of the infinite symmetric group over the field of rational functions in infinitely many variables.
Rohit Nagpal, Andrew Snowden
semanticscholar +1 more source