Symmetric group representations and Z

  title={Symmetric group representations and Z},
  author={Anshul Adve and Alexander Yong},
  journal={arXiv: Combinatorics},



The Symmetric Group

In this chapter, fundamentals of the symmetric group, namely, classes of permutations, Young diagrams, irreducible characters, and the construction of irreducible representations and their bases, are

The Representation Theory of the Symmetric Group

1. Symmetric groups and their young subgroups 2. Ordinary irreducible representations and characters of symmetric and alternating groups 3. Ordinary irreducible matrix representations of symmetric

On the Representation Theory of the Symmetric Groups

We present here a new approach to the description of finite-dimensional complex irreducible representations of the symmetric groups due to A. Okounkov and A. Vershik. It gives an alternative

Symmetric Functions Schubert Polynomials and Degeneracy Loci

Introduction The ring of symmetric functions Schubert polynomials Schubert varieties A brief introduction to singular homology Bibliography Index.

Representation Theory: A First Course

This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras. Following an introduction to representation

Representation theory

These are notes from the course MAT4270 on representation theory, autumn 2015. The lectures were held by Sergey Neshyevey. The notes are mine. The first half is about representations of finite

Construction of arbitrary Kazhdan-Lusztig polynomials in symmetric groups

To each polynomial P with integral nonnegative coefficients and constant term equal to 1, of degree d, we associate a certain pair of elements (y, w) in the symmetric group Sn, where n = 1 + d + P

Quiver coefficients are Schubert structure constants

We give an explicit natural identification between the quiver coefficients of Buch and Fulton, decomposition coefficients for Schubert polynomials, and the Schubert structure constants for flag

Asymptotics of characters of symmetric groups related to Stanley character formula

We prove an upper bound for characters of the symmetric groups. In particular, we show that there exists a constant a > 0 with a property that for every Young diagram with n boxes, r( ) rows and c( )

On the Analysis of the Kronecker Product of Irreducible Representations of the Symmetric Group

The Kronecker product of two irreducible matrix representations D (A), D (fi) of the symmetric group on n letters, furnishes a representation of that group, which is, in general reducible. The