Block characters of the symmetric groups

  • Authors:

  • Alexander Gnedin;Vadim Gorin;Sergei Kerov

  • Affiliations:

  • School of Mathematical Sciences, Queen Mary University of London, London, UK E1 4NS;Institute for Information Transmission Problems, Moscow, Russia 127994 and Massachusetts Institute of Technology, Cambridge, USA 02139;Institute for Information Transmission Problems, Moscow, Russia 127994 and Massachusetts Institute of Technology, Cambridge, USA 02139

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

Abstract

A block character of a finite symmetric group is a positive definite function which depends only on the number of cycles in a permutation. We describe the cone of block characters by identifying its extreme rays, and find relations of the characters to descent representations and the coinvariant algebra of ${\mathfrak{S}}_{n}$ . The decomposition of extreme block characters into the sum of characters of irreducible representations gives rise to certain limit shape theorems for random Young diagrams. We also study counterparts of the block characters for the infinite symmetric group ${\mathfrak{S}}_{\infty}$ , along with their connection to the Thoma characters of the infinite linear group GL 驴(q) over a Galois field.