Related papers: Generalized Weyl modules and Demazure submodules o…

In this paper, we give a characterization of the crystal bases $\mathcal{B}_{x}^{+}(\lambda)$, $x \in W_{\mathrm{af}}$, of Demazure submodules $V_{x}^{+}(\lambda)$, $x \in W_{\mathrm{af}}$, of a level-zero extremal weight module…

Let $\lambda \in P^{+}$ be a level-zero dominant integral weight, and $w$ an arbitrary coset representative of minimal length for the cosets in $W/W_{\lambda}$, where $W_{\lambda}$ is the stabilizer of $\lambda$ in a finite Weyl group $W$.…

For a nondegenerate additive subgroup $G$ of the $n$-dimensional vector space $F^n$ over an algebraically closed field $F$ of characteristic zero, there is an associative algebra and a Lie algebra of Weyl type $W(G,n)$ spanned by all…

For a dominant integral weight $lambda $, we introduce a family of $U_q ^+ (mathfrak{g})$-submodules $V_w (lambda)$ of the irreducible highest weight $U_q (mathfrak{g})$-module $V(lambda)$ of highest weight $lambda $ for a generalized…

We define a family of universal finite-dimensional highest weight modules for affine Lie algebras, we call these Weyl modules. We conjecture that these are the classical limits of the irreducible finite--dimensional representations of the…

We develop a general framework for studying relative weight representations for certain pairs consisting of an associative algebra and a commutative subalgebra. Using these tools we describe projective and simple weight modules for quantum…

We develop the theory of global and local Weyl modules for the hyperspecial maximal parabolic subalgebra of type $A_{2n}^{(2)}$. We prove that the dimension of a local Weyl module depends only on its highest weight, thus establishing a…

We study the properties of level zero modules over quantized affine algebras. The proof of the conjecture on the cyclicity of tensor products by Akasaka and the present author is given. Several properties of modules generated by extremal…

In this paper, we give a representation-theoretic interpretation of the specialization $E_{w_{\circ} \lambda} (q,\infty)$ of the nonsymmetric Macdonald polynomial $E_{w_{\circ} \lambda}(q,t)$ at $t=\infty$ in terms of the Demazure submodule…

Global Weyl modules for generalized loop algebras $\lie g\tensor A$, where $\lie g$ is a simple finite dimensional Lie algebra and A is a commutative associative algebra were defined, for any dominant integral weight $\lambda$, by…

For a finite Lie algebra $G_N$ of rank N, the Weyl orbits $W(\Lambda^{++})$ of strictly dominant weights $\Lambda^{++}$ contain $dimW(G_N)$ number of weights where $dimW(G_N)$ is the dimension of its Weyl group $W(G_N)$. For any…

We establish the existence of Demazure flags for graded local Weyl modules for hyper current algebras in positive characteristic. If the underlying simple Lie algebra is simply laced, the flag has length one, i.e., the graded local Weyl…

We study finite-dimensional respresentations of twisted current algebras and show that any graded twisted Weyl module is isomorphic to level one Demazure module for the twisted affine Kac-Moody algebra. Using the tensor product property of…

Let $\Lg$ be a simple complex Lie algebra, we denote by $\Lhg$ the corresponding affine Kac--Moody algebra. Let $\Lambda_0$ be the additional fundamental weight of $\Lhg$. For a dominant integral $\Lg$--coweight $\lam^\vee$, the Demazure…

We define Weyl functors, global modules for equivariant map Lie superalgebras $(\g \otimes A)^{\Gamma}$, where $\g$ is basic classical $\mathbb{C}$- Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}$-algebra. Under…

We determine the set of dominant $\ell$--weights in the Weyl (or standard) modules for quantum affine $A_n$. We then prove that the space of homomorphisms between standard modules is at most one-dimensional and give a necessary and…

Let g be a finite-dimensional complex simple Lie algebra. Fix a non-negative integer l, we consider the set of dominant weights {\lambda} of g such that l{\Lambda}_0+{\lambda} is a dominant weight for the corresponding untwisted affine…

We define global and local Weyl modules for $q \otimes A$, where $q$ is the queer Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}-$algebra. We prove that global Weyl modules are universal highest weight objects in…

In this paper we study general highest weight modules $\mathbb{V}^\lambda$ over a complex finite-dimensional semisimple Lie algebra $\mathfrak{g}$. We present three formulas for the set of weights of a large family of modules…

We prove that the category of finitely generated graded modules over the quiver Hecke algebra of arbitrary type admits numerous stratifications in the sense of Kleshchev. A direct consequence is that the full subcategory corresponding to…