Related papers: The Brundan-Kleshchev subalgebra and BK-type isomo…
In [Lu6] Lusztig defined a certain algebra $H,$ which is a direct sum of various algebras $H_{\mathfrak{o}}.$ We establish an explicit algebra isomorphism between each algebra $H_{\mathfrak{o}}$ and some matrix algebra with coefficients in…
Let $H_n(\boldsymbol{u})$ be the degenerate cyclotomic Hecke algebra with parameter $\boldsymbol{u}=(u_1, \ldots, u_m)$ over $\mathbb{C}(\boldsymbol{u})$. We define and construct the (non-)normalized Markov traces on the sequence…
In this article we introduce a framization of the Hecke algebra of type B. For this framization we construct a faithful tensorial representation and two linear bases. We finally construct a Markov trace on these algebras and from this trace…
We construct an explicit isomorphism between the generalised Khovanov arc algebras of type D and the basic algebras of the anti-spherical Hecke category associated to the maximal parabolic subgroup $W (A_{n-1})$ of $W (Dn)$. This…
Let $k$ be a field and suppose $p, q\in k$. We prove that the two affine Hecke algebras $H_q$ and $H_p$ of type $A_n$ are isomorphic as $k$-algebras if and only if $p=q^{\pm 1}$.
We consider Hilsum's notion of bordism as an equivalence relation on unbounded $KK$-cycles and study the equivalence classes. Upon fixing two $C^*$-algebras, and a $*$-subalgebra dense in the first $C^*$-algebra, a…
Affine Hecke algebras arise naturally in the study of smooth representations of reductive $p$-adic groups. Finite dimensional complex representations of affine Hecke algebras (under some restriction on the isogeny class and the parameter…
We construct a family of graded isomorphisms between certain subquotients of diagrammatic Cherednik algebras as the quantum characteristic, multicharge, level, degree, and weighting are allowed to vary; this provides new structural…
The affine and degenerate affine Birman-Murakami-Wenzl (BMW) algebras arise naturally in the context of Schur-Weyl duality for orthogonal and symplectic quantum groups and Lie algebras, respectively. Cyclotomic BMW algebras, affine and…
In this paper we consider the Hecke algebra $\mathcal {H}$ associated to an extended affine Weyl group of type $\widetilde{B_2}$. We give some interesting formulas on $C_{rt}S_{\lambda}$, which imply some relations between the…
The Khovanov-Lauda-Rouquier (KLR) algebra arose out of attempts to categorify quantum groups. Kleshchev and Ram proved a result reducing the representation theory of these algebras to the study of irreducible cuspidal representations. In…
We define analytic $R$-groups for affine Hecke algebras, and prove the analog of the Knapp-Stein Dimension Theorem. As a corollary we prove that the commutant algebra of a unitary principal series representation is isomorphic to the complex…
The Lascoux-Leclerc-Thibon conjecture, reformulated and solved by S. Ariki, asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup…
A commutative diagram that connects the basic objects of commutative algebra with the main objects of commutative analysis is constructed. Namely, with the help of five types of canonical embeddings we constructed a diagram between two sets…
We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting…
In the large rank limit, for any nonexceptional affine algebra, the graded branching multiplicities known as one-dimensional sums, are conjectured to have a simple relationship with those of type A, which are known as generalized Kostka…
We prove that the weighted KLRW algebras of finite type, and their cyclotomic quotients, are cellular algebras. The cellular bases are explicitly described using crystal graphs. As a special case, this proves that the KLR algebras of finite…
We construct a bigraded spectral sequence from the gl(0)-homology to knot Floer homology. This spectral sequence is of Bockstein type and comes from a subtle manipulation of coefficients. The main tools are quantum traces of foams and of…
Let $SL_{2n}$, $Sp_{2n}$, $E_6 = G^{sc}(E_6)$, $F_4 = G(F_4)$ be simply connected split algebraic groups over an arbitrary field $F$. Algebraic K-theory of affine homogeneous varieties $SL_{2n}/Sp_{2n}$ and $E_6/F_4$ is computed. Moreover,…
Let $F$ be a non-archimedean local field of residue characteristic $p\neq 2$. Let $G$ be a connected reductive group over $F$ that splits over a tamely ramified extension of $F$. Yu constructed types which are called tame supercuspidal…