We construct a pair of non-commutative rank 8 association schemes from 3 non-symmetric scheme. For the pair, two have same character table but different Frobenius-Schur indicators. This situation is similar to dihedral group and quaternion order 8. also determine structures adjacency algebras them over rational number field.

We introduce a generalized version of a q-Schur algebra (of parabolic type) for arbitrary Hecke algebras over extended Weyl groups. We describe how the decomposition matrix of a finite group with split BN -pair, with respect to a non-describing prime, can be partially described by the decomposition matrices of suitably chosen q-Schur algebras. We show that the investigated structures occur natu...

We introduce a generalized version of a q-Schur algebra (of parabolic type) for arbitrary Hecke algebras over extended Weyl groups. We describe how the decomposition matrix of a nite group with split BN-pair, with respect to a non-describing prime, can be partially described by the decomposition matrices of suitably chosen q-Schur algebras. We show that the investigated structures occur natural...

We study the notion of Schur multiplier a pair (N, L) Lie superalgebras and obtain some upper bounds concerning dimensions. Moreover, we characterize pairs finite dimensional (nilpotent) for whichfor t = 0; 1, where dim N (m|n).

We give sign-reversing involution proofs of a pair of two variable Pfaffian identities. Applications to symmetric function theory are given, including identities relating Pfaffians and Schur functions. As a corollary we are able to compute the plethysm p2 ° skn •

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...

For any continuous bilinear form defined on a pair of Hilbert spaces satisfying the compatibility Ladyshenskaya-Babušca-Brezzi condition, symmetric Schur complement operators can be defined on each of the two Hilbert spaces. In this paper, we find bounds for the spectrum of the Schur operators only in terms of the compatibility and continuity constants. In the light of the new spectral results ...

We establish a new Howe duality between a pair of two queer Lie superalgebras (q(m), q(n)). This gives a representation theoretic interpretation of a well-known combinatorial identity for Schur Q-functions. We further establish the equivalence between this new Howe duality and the Schur–Sergeev duality between q(n) and a central extension H̃k of the hyperoctahedral group Hk. We show that the zer...