Ricky Ini Liu

Matching polytopes and Specht modules

We prove that the dimension of the Specht module of a forest

Matrices with restricted entries and

G

q

is the same as the normalized volume of the matching polytope of

-analogues of permutations

G

On the commutative quotient of Fomin-Kirillov algebras

. We also associate to

Kronecker coefficients and noncommutative super Schur functions

G

A simplified Kronecker rule for one hook shape

a symmetric function

Subalgebras of the Fomin---Kirillov algebra

s_G

Specht modules and Schubert varieties for general diagrams

(analogous to the Schur symmetric function

Flow polytopes and the space of diagonal harmonics

s_\lambda