On Demazure and local Weyl modules for affine hyperalgebras

Abstract

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 modules are isomorphic to Demazure modules. This extends to the positive characteristic setting results of Chari-Loktev, Fourier-Littelmann, and Naoi for current algebras in characteristic zero. Using this result, we prove that the character of local Weyl modules for hyper loop algebras depend only on the highest weight, but not on the (algebraically closed) ground field, and deduce a tensor product factorization for them.

Finite-Dimensional Representations of Hyper Multicurrent and Multiloop Algebras

“…Finite-dimensional modules for hyper multicurrent algebras U F (g[n]). The results of this subsection generalizes for hyper multicurrent algebras (n > 1) some of the results of hyper current algebras (n = 1) from [6,Section 3.3 ], which was mainly motivated by [11]. The strategy is similar to [10].…”

“…In [7], the first author and Moura dealt with the twisted affine case. Hyperalgebras in the current algebra case and their connections with the loop algebra case and Demazure theory were studied by the first author in [6]. Throughout this work we denote by C, Z, Z + and N the sets of complex numbers, integers, nonnegative integers and positive integers, respectively.…”

“…, t ±1 n ] respectively, extending some of the known results in the case of current and loop algebras (g ⊗ C[t] and g ⊗ C[t ±1 ]). The approach for this is similar to [17,6], with the remark that the known characteristic zero methods as those compiled in [9] are not available for the hyperalgebra setting. We denote the multicurrent algebra in n variables by g[n] and the multiloop algebra by g n .…”

Modules with Demazure Flags and Character Formulae

“…Our paper gives a direct proof in the case of Demazure modules of affine sl 2 . This is essential in Naoi's work and is also needed in the recent preprint [2].…”

Limits of Multiplicities in Excellent Filtrations and Tensor Product Decompositions for Affine Kac-Moody Algebras

“…Both [26, Theorem A] and (2.4.2) were extended to the positive characteristic case in [2,10]. In particular, it follows from [2, Theorem 1.5.2(b)] that the multiplicities of Demazure modules in these flags are independent of the (algebraically closed) ground field.…”