Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Special Issue on the Representation Theory of the Symmetric Groups and Related Topics

The Guest Editors for this special issue are

Susanne Danz (Katholische Universität Eichstätt-Ingolstadt, Germany)
Andrew Mathas (University of Sydney, Australia)

The representation theory of the symmetric groups is a classical subject with its roots in the work of Schur and Young from the end of the 19th century. It is steeped in a rich and beautiful algebraic combinatorics, with close links to alternating groups and diagram algebras. It is also closely tied to the geometric representation theory of algebraic groups, Lie groups, Iwahori–Hecke algebras and Schur algebras. Recent exciting advances with KLR algebras show that the symmetric groups categorify the integral highest weight representations of Kac–Moody algebras and their crystal theory. This volume aims to showcase the rich and varied aspects of this theory.

The issue contains 9 papers with the total of 123 pages.

We wish to thank all the authors who have published papers in the issue, and to give our special thanks to all the referees for providing constructive reports.

The Guest Editors        

Papers in this Issue:

The Smallest Singular Values and Vector-Valued Jack Polynomials
Charles F. Dunkl
SIGMA 14 (2018), 115, 20 pages   [ abs   pdf ]
Morita Equivalent Blocks of Symmetric Groups
Benjamin Sambale
SIGMA 14 (2018), 100,   8 pages   [ abs   pdf ]
A Spin Analogue of Kerov Polynomials
Sho Matsumoto
SIGMA 14 (2018), 053, 13 pages   [ abs   pdf ]
Homomorphisms from Specht Modules to Signed Young Permutation Modules
Kay Jin Lim and Kai Meng Tan
SIGMA 14 (2018), 038, 21 pages   [ abs   pdf ]
The Duals of the 2-Modular Irreducible Modules of the Alternating Groups
John Murray
SIGMA 14 (2018), 033,   5 pages   [ abs   pdf ]
Billiards and Tilting Characters for ${\rm SL}_3$
George Lusztig and Geordie Williamson
SIGMA 14 (2018), 015, 22 pages   [ abs   pdf ]
Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution
Olivier Dudas and Nicolas Jacon
SIGMA 14 (2018), 007, 18 pages   [ abs   pdf ]
James' Submodule Theorem and the Steinberg Module
Meinolf Geck
SIGMA 13 (2017), 091,  6 pages   [ abs   pdf ]
Restriction of Odd Degree Characters of $\mathfrak{S}_n$
Christine Bessenrodt, Eugenio Giannelli and Jørn B. Olsson
SIGMA 13 (2017), 070, 10 pages   [ abs   pdf ]

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