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Computational Enumeration of Colorings of Hyperplanes of Hypercubes for all Irreducible Representations and Applications

open access: yesJournal of Mathematical Sciences and Modelling, 2018
We obtain the generating functions for the combinatorial enumeration of colorings of all hyperplanes of hypercubes for all irreducible representations of the hyperoctahedral groups.
Krishnan Balasubramanian
doaj   +2 more sources

On the irreducible representations of a finite semigroup [PDF]

open access: yesProceedings of the American Mathematical Society, 2009
Work of Clifford, Munn and Ponizovski{\u } parameterized the irreducible representations of a finite semigroup in terms of the irreducible representations of its maximal subgroups. Explicit constructions of the irreducible representations were later obtained independently by Rhodes and Zalcstein and by Lallement and Petrich.
Volodymyr Mazorchuk   +2 more
openaire   +5 more sources

On the classification of irreducible representations of real algebraic groups

open access: bronze, 1989
Suppose G is a connected reductive group over a global field F . Many of the problems of the theory of automorphic forms involve some aspect of study of the representation ρ of G(A(F )) on the space of slowly increasing functions on the homogeneous space
R. P. Langlands
openalex   +2 more sources

A Ribbon Hopf Algebra Approach to the Irreducible Representations of Centralizer Algebras: The Brauer, Birman–Wenzl, and Type A Iwahori–Hecke Algebras

open access: bronze, 1997
We show how the ribbon Hopf algebra structure on the Drinfel'd–Jimbo quantum groups of Types A, B, C, and D can be used to derive formulas giving explicit realizations of the irreducible representations of the Iwahori–Hecke algebras of type A and the ...
Robert Leduc, Arun Ram
openalex   +2 more sources

A note on representations of the finite Heisenberg group and sums of greatest common divisors [PDF]

open access: yesDiscrete Mathematics & Theoretical Computer Science, 2001
We review an elementary approach to the construction of all irreducible representations of the finite Heisenberg group. Determining the number of inequivalent classes of irreducible representations by different methods leads to an identity of sums ...
Johannes Grassberger, Günther Hörmann
doaj   +3 more sources

The Steinberg representation is irreducible

open access: yesDuke Mathematical Journal, 2023
28 pages, major revision, to appear in Duke Math ...
Putman, Andrew, Snowden, Andrew
openaire   +2 more sources

Local newforms for the general linear groups over a non-archimedean local field

open access: yesForum of Mathematics, Pi, 2022
In [14], Jacquet–Piatetskii-Shapiro–Shalika defined a family of compact open subgroups of p-adic general linear groups indexed by nonnegative integers and established the theory of local newforms for irreducible generic representations. In this paper, we
Hiraku Atobe   +2 more
doaj   +1 more source

Construction of matryoshka nested indecomposable N-replications of Kac-modules of quasi-reductive Lie superalgebras, including the sl(m/n) and osp(2/2n) series

open access: yesSciPost Physics Proceedings, 2023
We construct a new class of finite dimensional indecomposable representations of simple superalgebras which may explain, in a natural way, the existence of the heavier elementary particles.
Jean Thierry-Mieg, Peter D. Jarvis, Jerome Germoni, Maria Gorelik
doaj   +1 more source

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