Related papers: Demazure Characters and Affine Fusion Rules

We give a purely combinatorial derivation of Littelmann's refined Demazure character formula

We give new descriptions of the Bruhat order and Demazure products of affine Weyl groups in terms of the weight function of the quantum Bruhat graph. These results can be understood to describe certain closure relations concerning the…

The weights of finite-dimensional representations of simple Lie algebras are naturally associated with Weyl polytopes. Representation characters decompose into multiplicity-free sums over the weights in Weyl polytopes. The Brion formula for…

The Weyl-Kac character formula gives a beautiful closed-form expression for the characters of integrable highest-weight modules of Kac-Moody algebras. It is not, however, a formula that is combinatorial in nature, obscuring positivity. In…

This is an expository introduction to fusion rules for affine Kac-Moody algebras, with major focus on the algorithmic aspects of their computation and the relationship with tensor product decompositions. Many explicit examples are included…

The space spanned by the characters of twisted affine Lie algebras admit the action of certain congruence subgroups of $SL(2,\mathbb{Z})$. By embedding the characters in the space spanned by theta functions, we study an…

The Demazure product gives a natural monoid structure on any Coxeter group. Such structure occurs naturally in many different areas in Lie Theory. This paper studies the Demazure product of an extended affine Weyl group $\tilde W$. The main…

We derive the fusion rules for a basic series of admissible representations of $\hat{sl}(3)$ at fractional level $3/p-3$. The formulae admit an interpretation in terms of the affine Weyl group introduced by Kac and Wakimoto. It replaces the…

First, we prove the Kac-Wakimoto conjecture on modular invariance of characters of exceptional affine W-algebras. In fact more generally we prove modular invariance of characters of all lisse W-algebras obtained through Hamiltonian…

In vertex algebra theory, fusion rules are described as the dimension of the vector space of intertwining operators between three irreducible modules. We describe fusion rules in the category of weight modules for the Weyl vertex algebra.…

We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint…

We settle the fusion product decomposition theorem for higher-level affine Demazure modules for the cases $E^{(1)}_{6, 7, 8}, F^{(1)}_4$ and $E^{(2)}_{6}$, thus completing the main theorems of Chari et al. (J. Algebra, 2016) and Kus et al.…

It is known that characters of irreducible representations of finite Lie algebras can be obtained using theWeyl character formula including Weyl group summations which make actual calculations almost impossible except for a few Lie algebras…

Verlinde's formula for rational vertex operator algebras computes the fusion rules from the modular transformations of characters. In the non semisimple and non finite case, a logarithmic Verlinde formula has been proposed together with…

We study the unique maximal decomposition of an arbitrary affine permutation into a product of cyclically decreasing elements, providing a new perspective on work of Thomas Lam. This decomposition is closely related to the affine code,…

Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have an extended $W$ algebras which…

We study the structure of the finite-dimensional representations of $\mathfrak{sl}_2[t]$, the current Lie algebra type of $A_1$, which are obtained by taking tensor products of special Demazure modules. We show that these representations…

In this paper we study the family of prime irreducible representations of quantum affine $\lie{sl}_{n+1}$ which arise from the work of D. Hernandez and B. Leclerc. These representations can also be described as follows: the highest weight…

We present the first positive combinatorial rule for expanding the product of a permuted-basement Demazure atom and a Schur polynomial. Special cases of permuted-basement Demazure atoms include Demazure atoms and characters. These cases…

For an untwisted affine Kac-Moody Lie algebra $\mathfrak{g}$ with Cartan and Borel subalgebras $\mathfrak{h} \subset \mathfrak{b} \subset \mathfrak{g}$, affine Demazure modules are certain $U(\mathfrak{b})$-submodules of the irreducible…