140 citations · 609 across the 35 of their papers we have counts for
14 papers · 1 filter
Symmetric group characters of almost square shape
Sho Matsumoto, Piotr Śniady
We give closed product formulas for the irreducible characters of the symmetric groups related to rectangular `almost square' Young diagrams for a fixed value of an…
Random strict partitions and random shifted tableaux
Sho Matsumoto, Piotr Śniady
We study asymptotics of random shifted Young diagrams which correspond to a given sequence of reducible projective representations of the symmetric groups. We show limit results (L…
Linear versus spin: representation theory of the symmetric groups
Sho Matsumoto, Piotr Śniady
We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreduc…
Stanley character formula for the spin characters of the symmetric groups
Sho Matsumoto, Piotr Śniady
We give a new formula for the irreducible spin characters of the symmetric groups. This formula is analogous to Stanley's character formula for the usual (linear) characters of the…
A Spin Analogue of Kerov Polynomials
Sho Matsumoto
Kerov polynomials describe normalized irreducible characters of the symmetric groups in terms of the free cumulants associated with Young diagrams. We suggest well-suited counterpa…
Weingarten calculus via orthogonality relations: new applications
Benoît Collins, Sho Matsumoto
Weingarten calculus is a completely general and explicit method to compute the moments of the Haar measure on compact subgroups of matrix algebras. Particular cases of this calculu…
Polynomiality of shifted Plancherel averages and content evaluations
Sho Matsumoto
The shifted Plancherel measure is a natural probability measure on strict partitions. We prove a polynomiality property for the averages of the shifted Plancherel measure. As an ap…
Primitive factorizations, Jucys-Murphy elements, and matrix models
Sho Matsumoto, Jonathan Novak
A factorization of a permutation into transpositions is called "primitive" if its factors are weakly ordered. We discuss the problem of enumerating primitive factorizations of perm…
Jucys-Murphy elements, orthogonal matrix integrals, and Jack measures
Sho Matsumoto
We study symmetric polynomials whose variables are odd-numbered Jucys-Murphy elements. They define elements of the Hecke algebra associated to the Gelfand pair of the symmetric gro…
Jucys-Murphy Elements and Unitary Matrix Integrals
Sho Matsumoto, Jonathan Novak
In this paper, we study the relationship between polynomial integrals on the unitary group and the conjugacy class expansion of symmetric functions in Jucys-Murphy elements. Our ma…
Jack deformations of Plancherel measures and traceless Gaussian random matrices
Sho Matsumoto
We study random partitions of whose length is not bigger than a fixed number . Suppose a random partition is distributed according to the Jack meas…
Hyperdeterminantal expressions for Jack functions of rectangular shapes
Sho Matsumoto
We derive a Jacobi-Trudi type formula for Jack functions of rectangular shapes. In this formula, we make use of a hyperdeterminant, which is Cayley's simple generalization of the d…
Alpha-Pfaffian, pfaffian point process and shifted Schur measure
Sho Matsumoto
For any complex number and any even-size skew-symmetric matrix , we define a generalization $\pfaα(B)$ of the pfaffian $\pf(B)$ which we call the -pfaffian. The -pfaff…
Correlation functions of the shifted Schur measure
Sho Matsumoto
The shifted Schur measure introduced by Tracy and Widom is a measure on the set of all strict partitions, which is defined by Schur -functions. The main aim of this paper is to…