Related papers: Factorizations in Hecke algebras I: long cycle fac…
We study some quadratic algebras which are appeared in the low-dimensional topology and Schubert calculus. We introduce the Jucys-Murphy elements in the braid algebra and in the pure braid group, as well as the Dunkl elements in the…
A celebrated result of Farahat and Higman constructs an algebra $\mathrm{FH}$ which "interpolates" the centres $Z(\mathbb{Z}S_n)$ of group algebras of the symmetric groups $S_n$. We extend these results from symmetric group algebras to type…
We give a simple construction of Markov traces for Iwahori-Hecke algebras associated with infinite series of crystallographic Coxeter groups. In types B and D it is new, and generalizes a known construction in type A employing symmetric…
This paper is devoted to the computation of the number of ordered factorizations of a long cycle in the symmetric group where the number of factors is arbitrary and the cycle structure of the factors is given. Jackson (1988) derived the…
The $q$-deformed Araki-Woods von Neumann algebras $\Gamma_q(\mathcal{H}_\mathbb{R}, U_t)^{\prime \prime}$ are factors for all $q\in (-1,1)$ whenever $dim(\mathcal{H}_\mathbb{R})\geq 3$. When $dim(\mathcal{H}_\mathbb{R})=2$ they are factors…
We review some facts about the representation theory of the Hecke algebra. We adapt for the Hecke algebra case the approach of Okounkov and Vershik which was developed for the representation theory of symmetric groups. We justify an…
We consider graded Cartan matrices of the symmetric groups and the Iwahori-Hecke algebras of type A, which have entries in the ring $\mathbb Z[v,v^{-1}]$. These matrices may also be interpreted as Gram matrices of the Shapovalov form on…
We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations. Topics covered include…
In this paper we show that an affine Hecke algebra $H_q$ over complex numbers field with parameter $q\ne 1$ is not isomorphic to the group algebra over complex numbers field of the corresponding extend affine Weyl group if the corresponding…
We give a short proof, based on symmetric function theory, of a formula due to Goupil and Schaeffer, counting the number of factorizations of a cycle of maximal length in the symmetric group, into the product of two permutations of given…
We give closed-form formulas for the fundamental classes of degeneracy loci associated with vector bundle maps given locally by (not necessary square) matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal. Our…
We argue that one can factorize the difference equation of hypergeometric type on the nonuniform lattices in general case. It is shown that in the most cases of q-linear spectrum of the eigenvalues this directly leads to the dynamical…
We review known factorization results in quaternion matrices. Specifically, we derive the Jordan canonical form, polar decomposition, singular value decomposition, the QR factorization. We prove there is a Schur factorization for commuting…
We develop an inductive approach to the representation theory of the Yokonuma-Hecke algebra ${\rm Y}_{d,n}(q)$, based on the study of the spectrum of its Jucys-Murphy elements which are defined here. We give explicit formulas for the…
Let $H$ be a permutation group on a set $\Lambda$, which is permutationally isomorphic to a finite alternating or symmetric group $A_n$ or $S_n$ acting on the $k$-element subsets of points from $\{1,\ldots,n\}$, for some arbitrary but fixed…
Let $H^{\infty}(E)$ be a non commutative Hardy algebra, associated with a $W^*$-correspondence $E$. In this paper we construct factorizations of inner-outer type of the elements of $H^{\infty}(E)$ represented via the induced representation,…
We investigate various connections between the 0-Hecke monoid, Catalan monoid, and pattern avoidance in permutations, providing new tools for approaching pattern avoidance in an algebraic framework. In particular, we characterize…
We have studied the underlying algebraic structure of the anharmonic oscillator by using the variational perturbation theory. To the first order of the variational perturbation, the Hamiltonian is found to be factorized into a…
We introduce the spin Hecke algebra, which is a q-deformation of the spin symmetric group algebra, and its affine generalization. We establish an algebra isomorphism which relates our spin (affine) Hecke algebras to the (affine)…
Motivated by the Hankel determinant evaluation of moment sequences, we study a kind of Pfaffian analogue evaluation. We prove an LU-decomposition analogue for skew-symmetric matrices, called Pfaffian decomposition. We then apply this…