Related papers: Characters of Demazure modules and solvable lattic…
The weight systems of finite-dimensional representations of complex, simple Lie algebras exhibit patterns beyond Weyl-group symmetry. These patterns occur because weight systems can be decomposed into lattice polytopes in a natural way.…
Let $\mathfrak{g}$ be a finite-dimensional simple complex Lie algebra. A layer sum is introduced as the sum of formal exponentials of the distinct weights appearing in an irreducible $\mathfrak{g}$-module. It is argued that the character of…
We prove that the span of normalized characters of subprincipal admissible modules over an affine Lie algebra of subprincipal admissible level $k$ is $SL_2(\mathbf{Z})$-invariant and find the explicit modular transformation formula.
Spectra of suitably chosen Pisot-Vijayaraghavan numbers represent non-trivial examples of self-similar Delone point sets of finite local complexity, indispensable in quasicrystal modeling. For the case of quadratic Pisot units we…
Recently a remarkable map between 4-dimensional superconformal field theories and vertex algebras has been constructed \cite{BLLPRV15}. This has lead to new insights in the theory of characters of vertex algebras. In particular it was…
The goals of this article are as follows: (1) To determine the irreducible components of the affine varieties parametrizing the representations of $ \Lambda $ with dimension vector d, where $ \Lambda $ traces a major class of finite…
Starting from a detailed analysis of the structure of pathspaces of the ${\cal A}$-fusion graphs and the corresponding irreducible Virasoro algebra quotients $V(c,h)$ for the ($2,q$ odd) models, we introduce the notion of an admissible…
We use combinatorial description of bases of Feigin-Stoyanovsky's type subspaces of standard modules of level 1 for affine Lie algebras of types $A_\ell^{(1)}$ and $D_4^{(1)}$ to obtain character formulas. These descriptions naturally lead…
We show that the conformal characters of various rational models of W-algebras can be already uniquely determined if one merely knows the central charge and the conformal dimensions. As a side result we develop several tools for studying…
In 2015, the author proved combinatorially character formulas expressing sums of the (formal) dimensions of irreducible representations of symplectic groups, refining some works of Nekrasov and Okounkov, Han, King, and Westbury. In this…
The purpose of the present work is to describe a dequantization procedure for topological modules over a deformed algebra. We define the characteristic variety of a topological module as the common zeroes of the annihilator of the…
We derive formulas for characterizing bounded orthogonally additive polynomials in two ways. Firstly, we prove that certain formulas for orthogonally additive polynomials derived in \cite{Kusa} actually characterize them. Secondly, by…
We consider various specializations of the non-twisted quantum affine algebras at roots of unity. We define and study the q-characters of their finite-dimensional representations.
In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on…
Let us consider a specialization of an untwisted quantum affine algebra of type $ADE$ at a nonzero complex number, which may or may not be a root of unity. The Grothendieck ring of its finite dimensional representations has two bases,…
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…
We express the multiplicities of the irreducible summands of certain tensor products of irreducible integrable modules for an affine Kac-Moody algebra over a simply laced Lie algebra as sums of multiplicities in appropriate excellent…
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…
An explicit lattice point realization is provided for the primary components of an arbitrary binomial ideal in characteristic zero. This decomposition is derived from a characteristic-free combinatorial description of certain primary…
We study sums of the form $\sum_{k=m}^n a_{nk} b_{km}$, where $a_{nk}$ and $b_{km}$ are binomial coefficients or unsigned Stirling numbers. In a few cases they can be written in closed form. Failing that, the sums still share many common…