Geodesic
Block characters of the symmetric groups.
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 1, pp. 79-101.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $_{\infty }(q)$ over a Galois field.
Keywords: symmetric group, characters, coinvariant algebra, limit shape 
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Gnedin, Alexander; Gorin, Vadim; Kerov, Sergei. Block characters of the symmetric groups.. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 1, pp. 79-101. http://geodesic.mathdoc.fr/item/JAC_2013__38_1_a6/