In the late 1930’s Murnaghan discovered the existence of a stabilization phenomenon for the Kronecker product of Schur functions. For n large enough, the values of the Kronecker coefficients appearing in the product of two Schur functions of degree n do not depend on the first part of the indexing partitions, but only on the values of their remaining parts. We compute the exact value of n when ...

By a result of Schur [J. Reine Angew. Math. 140 (1911), pp. 1–28], the entrywise product M ? N M \circ N</mml:annotatio...

Abstract We define operator-valued Schur and Herz–Schur multipliers in terms of module actions, show that the standard properties these follow from well-known facts about actions duality theory for group actions. These results are applied to study an abelian acting on its Pontryagin dual: it is shown a natural subset can be identified with classical direct product dual group.

We investigate the Hadamard product of inverse M-matrices and present two classes of inverse M-matrices that are closed under the Hadamard multiplication. In the end, we give some inequalities on the Fan product of M-matrices and Schur complements. © 2000 Elsevier Science Inc. All rights reserved. AMS classification: 15A09; 15A42

We give a combinatorial description of the composition factors of the induction product of two evaluation modules of the affine Iwahori-Hecke algebra of type GLm. Using quantum affine Schur-Weyl duality, this yields a combinatorial description of the composition factors of the tensor product of two evaluation modules of the quantum affine algebra Uq(ŝln).

A new polynomial analogue of the Rogers–Ramanujan identities is proven. Here the product-side of the Rogers–Ramanujan identities is replaced by a partial theta sum and the sum-side by a weighted sum over Schur polynomials.

A new type of polynomial analogue of the Rogers–Ramanujan identities is proven. Here the product-side of the Rogers–Ramanujan identities is replaced by a partial theta sum and the sum-side by a weighted sum over Schur polynomials.

We systematically study wreath product Schur functions and give a combinatorial construction using colored partitions and tableaux. The Pieri rule and the Littlewood-Richardson rule are studied. We also discuss the connection with representations of generalized symmetric groups.

John Stembridge [St] has recently solved the important problem of finding a “Littlewood-Richardson rule” for Q-functions. His proof is very natural combinatorially, but lengthy, if all the background is included. It uses extensive material from Worley’s thesis [W] and Sagan’s similar theory of shifted tableaux [Sa]. To include this result in a forthcoming book (coauthored by John Humphreys), an...