We prove that structure constants related to Hecke algebras at roots of unity are special cases of k-Littlewood-Richardson coefficients associated to a product of k-Schur functions. As a consequence, both the 3point Gromov-Witten invariants appearing in the quantum cohomology of the Grassmannian, and the fusion coefficients for the WZW conformal field theories associated to ŝu( ) are shown to b...

Let S (Λ) be the cyclotomic q-Schur algebra associated to the ArikiKoike algebra Hn,r, introduced by Dipper-James-Mathas. In this paper, we consider v-decomposition numbers of S (Λ), namely decomposition numbers with respect to the Jantzen filtrations of Weyl modules. We prove, as a v-analogue of the result obtained by Shoji-Wada, a product formula for v-decomposition numbers of S (Λ), which as...

In this paper, we establish Schur-Weyl reciprocity for the q-analogue of the alternating group. We analyze the sign q-permutation representation of the Hecke algebra HQ(q),r(q) on the rth tensor product of Z2-graded Q-vector space V = V0⊗V1 in detail, and examine its restriction to the qanalogue of the alternating group H1Q(q),r(q). In consequence, we find out that if dimV0 = dimV1, then the ce...

The Kronecker product of two homogeneous symmetric polynomials P1 and P2 is defined by means of the Frobenius map by the formula P1 ⊗ P2 = F (F−1P1)(F−1P2). When P1 and P2 are Schur functions sλ and sμ respectively, then the resulting product sλ ⊗ sμ is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the diagrams λ an...

We apply support vector learning to attributed graphs where the kernel matrices are based on approximations of the Schur-Hadamard inner product. The evaluation of the Schur-Hadamard inner product for a pair of graphs requires the determination of an optimal match between their nodes and edges. It is therefore efficiently approximated by means of recurrent neural networks. The optimal mapping in...

A bijective proof of the product formula for the principal specialization of super Schur functions (also called hook Schur functions) is given using the combinatorial description of super Schur functions in terms of certain tableaux due to Berele and Regev. Our bijective proof is based on the Hillman–Grassl algorithm and a modified version of Schützenberger’s jeu de taquin. We then explore the ...

In this work, we made progress on the problem that [ symbol: see text] is a Banach algebra under schur product. Our results extend Tonge's results. We also obtained estimates for the norm of the random quadralinear form A:l(r)(M) x l(p)(N) x l(q)(K) x l(s)(H)-->C, defined by: A(e(i), e(j), e(k), e(s))=a(ijks), where the (a(ijks))'s are uniformly bounded, independent, mean zero random variables....