Related papers: On polyhedral formulas for Kirillov-Reshetikhin mo…

A method for the analytical evaluation of layer potentials arising in the collocation boundary element method for the Laplace and Helmholtz equation is developed for piecewise flat boundary elements with polynomial shape functions. The…

We show that the category O for a rational Cherednik algebra of type A is equivalent to modules over a q-Schur algebra (parameter not a half integer), providing thus character formulas for simple modules. We give some generalization to…

We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic…

We obtain character formulas of minimal affinizations of representations of quantum groups when the underlying simple Lie algebra is orthogonal and the support of the highest weight is contained in the first three nodes of the Dynkin…

We reprove the results of Jordan [18] and Siebert [31] and show that the Lie algebra of polynomial vector fields on an irreducible affine variety X is simple if and only if X is a smooth variety. Given proof is self-contained and does not…

We give a uniform description of the bijection $\Phi$ from rigged configurations to tensor products of Kirillov--Reshetikhin crystals of the form $\bigotimes_{i=1}^N B^{r_i,1}$ in dual untwisted types: simply-laced types and types…

We extend the techniques in arXiv:2209.08865(1) to the non-simply-laced situation, and calculate explicit special values of parabolic affine inverse Kazhdan-Lusztig polynomials for subregular nilpotent orbits. We thus obtain explicit…

We construct modular categories from Hecke algebras at roots of unity. For a special choice of the framing parameter, we recover the Reshetikhin-Turaev invariants of closed 3-manifolds constructed from the quantum groups U_q sl(N) by…

The authors proved that a Weyl module for a simple algebraic group is irreducible over every field if and only if the module is isomorphic to the adjoint representation for $E_{8}$ or its highest weight is minuscule. In this paper, we prove…

For convex sets $K$ and $L$ in ${\mathbb{R}}^d$ we define $R_L(K)$ to be the convex hull of all points belonging to $K$ but not to the interior of $L$. Cutting-plane methods from integer and mixed-integer optimization can be expressed in…

We construct all finite irreducible modules over Lie conformal superalgebras of type K

A classical result of A. Connes asserts that the Frechet algebra of smooth functions on a smooth compact manifold X provides, by a purely algebraic procedure, the de Rham cohomology of X. Namely the procedure uses Hochschild and cyclic…

In this note, we formulate and prove branching rules of simple polynomial modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. Our branching rules depend on the conjugacy class of the Borel subalgebra. A Gelfand-Tsetlin basis of a…

In this article we investigate Hirzebruch-Riemann-Roch formulae for line bundles on irreducible symplectic K\"ahler manifolds. As Huybrechts has shown, for every irreducible complex K\"ahler manifold $X$ of dimension $2n$, there are numbers…

Let $G$ be a simple, simply connected algebraic group over an algebraically closed field of prime characteristic $p>0$. Recent work of Kildetoft and Nakano and of Sobaje has shown close connections between two long-standing conjectures of…

We explain a strategy for a proof of the positivity of all coefficients of Kazhdan-Lusztig-polynomials for arbitrary Coxeter groups by constructing spaces whose dimensions we conjecture to be these coefficients.

We use the differential algebra of polytopes to explain the known remarkable relation of the combinatorics of the associahedra and permutohedra with the universal compositional and multiplicative inversion formulas for the formal power…

A combinatorial description of the crystal $\mathcal{B}(\infty)$ for finite-dimensional simple Lie algebras in terms of Young tableaux was developed by J. Hong and H. Lee. Using this description, we obtain a combinatorial rule for…

We solve the discrete Hirota equations (Kirillov-Reshetikhin Q-systems) for $A_r$, and their analogue for $D_r$, for the cases where the second variable ranges over either a finite set or over all integers. Until now only special solutions…

We construct a combinatorial crystal structure on the Kirillov-Reshetikhin crystal $B^{7,s}$ in type $E_7^{(1)}$, where $7$ is the unique node in the orbit of $0$ in the affine Dynkin diagram. We then describe the combinatorial $R$-matrix…