Related papers: A twining character formula for Demazure modules (…

We define a Dieudonn\'e module as the module of Dieudonn\'e elements, and set up Dieudonn\'e module theory in a simple way. Under this formulation we give explicit formulae for the duality and the corresponding differential operators.

We study, in the path realization, crystals for Demazure modules of affine Lie algebras of types $A^{(1)}_n,B^{(1)}_n,C^{(1)}_n,D^{(1)}_n, A^{(2)}_{2n-1},A^{(2)}_{2n}, and D^{(2)}_{n+1}$. We find a special sequence of affine Weyl group…

The Demazure operator associated to a simple reflection satisfies the twisted Leibniz rule. In this paper we introduce a generalization of the twisted Leibniz rule for the Demazure operator associated to any atomic double coset. We prove…

We study the tensor product of Demazure crystals for symmetrizable Kac-Moody Lie algebras. It is not necessary that the tensor product of Demazure crystals is isomorphic to a disjoint union of Demazure crystals. In this paper, we provide…

For $G$ a reductive group and $T\subset B$ a maximal torus and Borel subgroup, Demazure modules are certain $B$-submodules, indexed by elements of the Weyl group, of the finite irreducible representations of $G$. In order to describe the…

We establish a character formula for indecomposable tilting modules for connected reductive groups in characteristic p in terms of p-Kazhdan-Lusztig polynomials, for p>h the Coxeter number. Using results of Andersen, one may deduce a…

We provide an exact formula for the complex exponents in the modular product expansion of the modular units, and deduce a characterization of the modular units in terms of the growth of these exponents, answering a question of W. Kohnen.

We give an explicit, nonnegative formula for the expansion of nonsymmetric Macdonald polynomials specialized at $t=0$ in terms of Demazure characters. Our formula results from constructing Demazure crystals whose characters are the…

We obtain a characteristic-free decomposition of tensor space, regarded as a module for the Brauer centralizer algebra.

We prove an explicit version of Burgess' bound on character sums for composite moduli.

The classical Pieri formula gives a multiplicity free expansion of an irreducible module with a fundamental one for the complex general linear group. In this article we replace the tensor product by the fusion product and prove an analogue…

We give a decomposition formula for computing the state polytope of a reducible variety in terms of the state polytopes of its components.

Let G be a semisimple group over an algebraically closed field of characteristic p>0. We give a (partly conjectural) simple, closed formula for the character of many indecomposable tilting rational G-modules, assuming that p is large.

The product monomial crystal was defined by Kamnitzer, Tingley, Webster, Weekes, and Yacobi for any semisimple simply-laced Lie algebra $\mathfrak{g}$, and depends on a collection of parameters $\mathbf{R}$. We show that a family of…

We characterize, in the case of affine sl(2), the crystal base of the Demazure module E_w(\La) in terms of extended Young diagrams or paths for any dominant integral weight \La and Weyl group element w. Its character is evaluated via two…

For an untwisted affine Lie algebra we prove an embedding of any higher level Demazure module into a tensor product of lower level Demazure modules (e.g. level one in type A) which becomes in the limit (for anti-dominant weights) the…

In this paper, we obtain a restricted decomposition formula for interpolated multiple zeta values using t-stuffle product. We then derive a recursive formula of t-stuffle product, which also provides a route to the same formula. In both…

We obtain a multiplication formula for cluster characters on (stably) 2-Calabi-Yau (Frobenius or) triangulated categories. This formula generalizes those known for arbitrary pairs of objects and for Auslander-Reiten triangles. As an…

We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group $\SL_2$, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands.…

We prove a formula for special L-values of Anderson's modules, analogue in positive characteristic of the class number formula. We apply this result to two kinds of L-series.