相关论文: The cyclotomic BMW algebra associated with the two…

We prove a conjecture of the first and third named authors relating the Kauffman bracket skein algebra of a genus zero surface with boundary to a quantized $K$-theoretic Coulomb branch. As a consequence, we see that our skein algebra arises…

Let $W$ be a Coxeter group. The goal of the paper is to construct new Hopf algebras that contain Hecke algebras $H_{\bf q}(W)$ as (left) coideal subalgebras. Our Hecke-Hopf algebras ${\bf H}(W)$ have a number of applications. In particular…

We study representations of the loop braid group $LB_n$ from the perspective of extending representations of the braid group $B_n$. We also pursue a generalization of the braid/Hecke/Temperlely-Lieb paradigm---uniform finite dimensional…

In the same way the folding of the Dynkin diagram of A_{2n} (resp. A_{2n-1}) produces the B_n (resp. C_n) Dynkin diagram, the symmetry algebra W of a Toda model based on B_n (resp. C_n) can be seen as resulting from the folding of a…

Motivated by Brundan-Kleshchev's work on higher Schur-Weyl duality, we establish mixed Schur-Weyl duality between general linear Lie algebras and cyclotomic walled Brauer algebras in an arbitrary level. Using weakly cellular bases of…

A set of ring generators for the Hecke algebra of the Gel'fand pair $(S_{2n},B_n)$, where $B_n$ is the hyperoctahedral subgroup of the symmetric group $S_{2n}$ is presented. Various corollaries are given. A conjecture of Sho Matsumoto is…

The Hecke algebra of the pair $(S_{2n},B_n)$, where $B_n$ is the hyperoctahedral subgroup of $S_{2n}$, was introduced by James in 1961. It is a natural analogue of the center of the symmetric group algebra. In this paper, we give a…

In \cite{GS1} the notion of braided Yangians of Reflection Equation type was introduced. Each of these algebras is associated with an involutive or Hecke symmetry $R$. Besides, the quantum analogs of certain symmetric polynomials…

We construct a 2-representation categorifying the symmetric Howe representation of $\mathfrak{gl}_m$ using a deformation of an algebra introduced by Webster. As a consequence, we obtain a categorical braid group action taking values in a…

Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided…

We develop a cyclotomic analogue of the theory of associators. Using a trigonometric version of the universal KZ equations, we prove the formality of a morphism B_n^1 -> (ZZ/N ZZ)^n rtimes S_n, where B_n^1 is a braid group of type B. The…

Ariki's and Grojnowski's approach to the representation theory of affine Hecke algebras of type $A$ is applied to type $B$ with unequal parameters to obtain -- under certain restrictions on the eigenvalues of the lattice operators --…

A new type of algebras that represent a generalization of both quantum groups and braided groups is defined. These algebras are given by a pair of solutions of the Yang--Baxter equation that satisfy some additional conditions. Several…

We define alternating cyclotomic Hecke algebras in higher levels as subalgebras of cyclotomic Hecke algebras under an analogue of Goldman's hash involution. We compute the rank of these algebras and construct a full set of irreducible…

The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…

A new basis of the $q$-Brauer algebra is introduced, which is a lift of Murphy bases of Hecke algebras of symmetric groups. This basis is a cellular basis in the sense of Graham and Lehrer. Subsequently, using combinatorial language we…

These lectures given in Montreal in Summer 1997 are mainly based on, and form a condensed survey of, the book by N. Chriss and V. Ginzburg: `Representation Theory and Complex Geometry', Birkhauser 1997. Various algebras arising naturally in…

We study analogues of Jucys-Murphy elements in cellular algebras arising from repeated Jones basic constructions. Examples include Brauer and BMW algebras and their cyclotomic analogues.

We prove Schur--Weyl duality between the Brauer algebra $\mathfrak{B}_n(m)$ and the orthogonal group $O_{m}(K)$ over an arbitrary infinite field $K$ of odd characteristic. If $m$ is even, we show that each connected component of the…

The mixed braid groups $B_{2,n}, \ n \in \mathbb{N}$, with two fixed strands and $n$ moving ones, are known to be related to the knot theory of certain families of $3$-manifolds. In this paper we define the mixed Hecke algebra…