In this paper, we define the higher Frobenius-Schur (FS-)indicators for finite-dimensional modules of a semisimple quasi-Hopf algebra H via the categorical counterpart developed in a 2005 preprint. When H is an ordinary Hopf algebra, we show that our definition coincides with that introduced by Kashina, Sommerhäuser, and Zhu. We find a sequence of gauge invariant central elements of H such that...

This paper proves an identity between flagged Schur polynomials, giving a duality row flags and column flags. generalises both the binomial determinant theorem due to Gessel Viennot symmetric function Aitken. As corollaries we obtain lifts of \(q\)-binomial coefficients polynomials. Our method is path counting argument on novel lattice generalising that used by Viennot.

We define the radical and weight of a skew left brace provide some basic properties these notions. In particular, we obtain Wedderburn type decomposition for Artinian braces. Furthermore, prove analogues theorem Wiegold, Schur its converse in context Finally, apply results to detect torsion structure group finite bijective non-degenerate set-theoretic solution Yang–Baxter equation.

and Applied Analysis 3 where L x, y , I x, y denote logarithmic mean and identric exponential mean, respectively, G a, b √ ab. The Schur convexity of Sp,q a, b and Gp,q a, b on 0,∞ × 0,∞ with respect to a, b was investigated by Qi et al. 4 , Shi et al. 5 , Li and Shi 6 , and Chu and Zhang 7 . Until now, they have been perfectly solved by Chu and Zhang 7 , Wang and Zhang 8 , respectively. Recent...

The paper studies the eigenvalue distribution of Schur complements of some special matrices, including nonstrictly diagonally dominant matrices and general H−matrices. Zhang, Xu, and Li [Theorem 4.1, The eigenvalue distribution on Schur complements of H-matrices. Linear Algebra Appl., 422:250–264, 2007] gave a condition for an n×n diagonally dominant matrix A to have |JR+(A)| eigenvalues with p...

1 , . . . , xn, x −1 n factorizes into a product of two odd orthogonal characters of rectangular shape, one of which is evaluated at −x1, . . . ,−xn, if M is even, while it factorizes into a product of a symplectic character and an even orthogonal character, both of rectangular shape, if M is odd. It is furthermore shown that the first factorization implies a factorization theorem for rhombus t...

Let F denote the Fock space representation of the quantum groupUv(ŝle). The ‘v-decomposition numbers’ are the coefficients when the canonical basis for this representation is expanded in terms of the basis of partitions, and the evaluations at v = 1 of these polynomials give the decomposition numbers for Iwahori–Hecke algebras and q-Schur algebras over C. James and Mathas have proved a theorem ...

Various important weighted polynomial inequalities, such as Bernstein, Marcinkiewicz, Nikolskii, Schur, Remez, etc. inequalities, have been proved recently by Giuseppe Mastroianni and Vilmos Totik under minimal assumptions on the weights. In most of the cases this minimal assumption is the doubling condition. Here, based on a recently proved Bernstein-type inequality by D.S. Lubinsky, we establ...