Block characters of the symmetric groups
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10801_2012_Article_394.pdf
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Author(s)
Gnedin, Alexander
Gorin, Vadim
Kerov, Sergei
Date Issued
August 2012
Journal
Journal of Algebraic Combinatorics
Publisher
Springer US
Citation
Gnedin, Alexander, Vadim Gorin, and Sergei Kerov. “Block Characters of the Symmetric Groups.” Journal of Algebraic Combinatorics 38.1 (2013): 79–101.
Version
Author's final manuscript
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 S[subscript 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 S[subscript n], along with their connection to the Thoma characters of the infinite linear group GL[subscript ∞](q) over a Galois field.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10801-012-0394-9
