Related papers: Classification of irreducible $\mathfrak{u}$-diago…

In this paper we construct finite dimensional representations of the wreath product symplectic reflection algebra H(k,c,N,G) of rank N attached to a finite subgroup G of SL(2,C) (here k is a number and c a class function on the set of…

We develop the theory of a category ${\mathscr C}_A$ which is a generalisation to non-restricted ${\mathfrak g}$-modules of a category famously studied by Andersen, Jantzen and Soergel for restricted ${\mathfrak g}$-modules, where…

We prove some basic results about irreducible components of varieties of modules for an arbitrary finitely generated associative algebra. Our work generalizes results of Kac and Schofield on representations of quivers, but our methods are…

We consider finite W-algebras U(g,e) associated to even multiplicity nilpotent elements in classical Lie algebras. We give a classification of finite dimensional irreducible U(g,e)-modules with integral central character in terms of the…

In paper, we study the representation theory of super $W(2,2)$ algebra ${\mathfrak{L}}$. We prove that ${\mathfrak{L}}$ has no mixed irreducible modules and give the classification of irreducible modules of intermediate series. We…

The Deligne-Langlands correspondence parametrizes irreducible representations of the affine Hecke algebra $\mathcal{H}^{\text{aff}}$ by certain perverse sheaves. We show that this can be lifted to an equivalence of triangulated categories.…

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields with residual characteristic $p\neq2$, and $\ell$ be a prime number different from $p$. We classify those $\ell$-modular cuspidal irreducible representations of…

In this paper we classify irreducible integrable representations of loop toroidal Lie algebras with finite dimensional weight spaces. In both the cases we classify modules, when a part of center acts non-trivially and trivially on modules.

Let ${\mathfrak g}$ be a finite dimensional Lie algebra over a field of characteristic 0, with solvable radical ${\mathfrak r}$ and nilpotent radical ${\mathfrak n}=[{\mathfrak g},{\mathfrak r}]$. Given a finite dimensional ${\mathfrak…

We show that in ADE type the trace of Webster's categorification of a tensor product of irreducibles for the quantum group is isomorphic to a tensor product of Weyl modules for the current algebra $\dot{U}(\mathfrak{g}[t])$. This extends a…

We prove that irreducible representations of the elliptic affine Hecke algebras of Ginzburg, Kapranov, and Vasserot are in one-to-one correspondence with certain nilpotent Higgs bundles on the elliptic curve. The main tool we use is the…

Let F_0 be a non-archimedean local field of odd residual characteristic and let G be the non quasi-split unramified unitary group in four variables defined over F_0. In this paper, we give a classification of the irreducible smooth…

We compute the image of a polynomial $GL_N$-module under the Etingof-Freund-Ma functor \cite{EFM}. We give a combinatorial description of the image in terms of standard tableaux on a collection of skew shapes and analyze weights of the…

This note extends some results of a previous paper (math.RT/0403250) about finite dimensional representations of the wreath product symplectic reflection algebra H(k,c,N,G) of rank N attached to a finite subgroup G of SL(2,C) (here k is a…

We show that the Young tableaux theory and constructions of the irreducible representations of the Weyl groups of type A, B and D, Iwahori-Hecke algebras of types A, B, and D, the complex reflection groups G(r,p,n) and the corresponding…

We consider the problem of classifying irreducible Specht modules for the Iwahori-Hecke algebra of type B with parameters Q,q. We solve this problem completely in the case where q is not a root of unity, and in the case q=-1 we reduce the…

Rao and Zhao classified the irreducible integrable modules with finite dimensional weight spaces for the untwisted affine superalgebras which are not $\hat{A}(m,n)$ ($m\ne n$) or $\hat{C}(m)$. Here we treat the latter affine superalgebras…

We give a classification of the simple modules for the cyclotomic Hecke algebras over $\mathbb{C}$ in the modular case. We use the unitriangular shape of the decomposition matrices of Ariki-Koike algebras and Clifford theory.

We give a $K$-theoretic realization of all affine Hecke algebras with two unequal parameters including exceptional types. This extends the celebrated work of Kazhdan and Lusztig, who gave a $K$-theoretic realization of affine Hecke algebras…

The so called quantized algebras of functions on affine Hecke algebras of type A and the corresponding q-Schur algebras are defined and their irreducible unitarizable representations are classified.