Upper Bound on the Characters of the Symmetric Groups for Balanced Young Diagrams and a Generalized Frobenius Formula
نویسندگان
چکیده
We study asymptotics of an irreducible representation of the symmetric group Sn corresponding to a balanced Young diagram λ (a Young diagram with at most O( √ n) rows and columns) in the limit as n tends to infinity. We find an optimal asymptotic bound for characters χ(π). Our main achievement is that—contrary to previous results in this direction—we do not assume that the length |π| of the permutation is small in comparison to n. Our main tool is an analogue of Frobenius character formula which holds true not only for cycles but for arbitrary permutations.
منابع مشابه
Asymptotics of Characters of Symmetric Groups Related to Skew Young Diagrams and Generalized Stanley-féray Character Formula
We show that a generalization of Stanley-Féray character formula for characters of symmetric groups holds true for skew Young diagrams. This generalization is very useful for dealing with asymptotic questions; for example we use it to show that balanced skew Young diagrams have the asymptotic property of approximate factorization of characters and therefore the fluctuations of a randomly select...
متن کاملUpper Bound on Characters of Symmetric Groups Based on Stanley-féray Character Formula
We prove an of upper bound for characters of the symmetric groups based on a recent character formula which was conjectured by Stanley and proved by Féray. Namely, we show that there exists a constant a > 0 with a property that for every Young diagram λ with n boxes, r(λ) rows and c(λ) columns
متن کاملGeneralized Characters of the Symmetric Group
Normalized irreducible characters of the symmetric group S(n) can be understood as zonal spherical functions of the Gelfand pair (S(n)×S(n),diag S(n)). They form an orthogonal basis in the space of the functions on the group S(n) invariant with respect to conjugations by S(n). In this paper we consider a different Gelfand pair connected with the symmetric group, that is an “unbalanced” Gelfand ...
متن کاملREPRESENTATIONS OF THE SYMMETRIC GROUPS AND COMBINATORICS OF THE FROBENIUS-YOUNG CORRESPONDENCE By MATTHEW
After introducing the concepts of partitions, Young diagrams, representation theory, and characters of representations, the 2006 paper by A. M. Vershik entitled “A New Approach to the Representation Theory of the Symmetric Group, III: Induced Representations and the Frobenius-Young Correspondence” is discussed. In tracing through Vershik’s line of reasoning, a flaw emerges in his attempt to pro...
متن کاملA generalized upper bound solution for bimetallic rod extrusion through arbitrarily curved dies
In this paper, an upper bound approach is used to analyze the extrusion process of bimetallic rods through arbitrarily curved dies. Based on a spherical velocity field, internal, shearing and frictional power terms are calculated. The developed upper bound solution is used for calculating the extrusion force for two types of die shapes: a conical die as a linear die profile and a streamlined di...
متن کامل