Related papers: Non-Gatherable Triples for Non-Affine Root Systems

We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change,…

An affine Hecke algebra H contains a large abelian subalgebra A. The center Z of H is the subalgebra of Weyl group invariant elements in A. The natural trace of the affine Hecke algebra can be written as an integral of a rational $n$ form…

We prove a family of 3-term relations in the Grothendieck ring of the category of finite-dimensional modules over the affine quantum algebra of type $G_2$ extending the celebrated $T$-system relations of type $G_2$. We show that these…

We present the algebraic classification of the gravitational field in four-dimensional general metric-affine geometries, thus extending the current results of the literature in the particular framework of Weyl-Cartan geometry by the…

The first part of this work uses the algorithm recently detailed in arXiv:1906.02935 to classify the irreducible weight modules of the minimal model vertex operator algebra $L_k(\mathfrak{sl}_3)$, when the level $k$ is admissible. These are…

Let $F$ be a non-Archimedian local field of characteristic zero and $E/F$ a quadratic extension. The aim of the present article is to study the multiplicity of an irreducible admissible representation of ${\rm GL}_2(F)$ occurring in an…

We obtain a new free field realization of $N=2$ super $W_{3}$ algebra using the technique of quantum hamiltonian reduction. The construction is based on a particular choice of the simple root system of the affine Lie superalgebra…

We give a presentation of localized affine and degenerate affine Hecke algebras of arbitrary type in terms of weights of the polynomial subalgebra and varied Demazure-BGG type operators. We offer a definition of a graded algebra…

We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is known when the…

A myriad of irreducible symplectic 4-manifolds with abelian non-cyclic fundamental group is constructed. The botany of manifolds with finite non-cyclic fundamental groups is also studied.

There is a long history of studying Ramsey theory using the algebraic structure of the Stone-\v{C}ech compactification of discrete semigroup. It has been shown that various Ramsey theoretic structures are contained in different algebraic…

In this paper we consider the Hecke algebra $\mathcal {H}$ associated to an extended affine Weyl group of type $\widetilde{B_2}$. We give some interesting formulas on $C_{rt}S_{\lambda}$, which imply some relations between the…

The algorithm of computing generalized Green functions of a finite reductive group contains some unkonwn scalars occuring from the F_q structure of irreducible local systems on unipotent classes on G. In this paper, we determine such…

(1) Every infinite, Abelian compact (Hausdorff) group K admits 2^|K|-many dense, non-Haar-measurable subgroups of cardinality |K|. When K is nonmetrizable, these may be chosen to be pseudocompact. (2) Every infinite Abelian group G admits a…

Let w be an element of the Weyl group of a reductive group G defined and split over a finite field. We consider the variety of triples (g,B,B') where g is a unipotent element of G and B, B' are Borel subgroups of G such that B contains g…

We establish a connection between (degenerate) nonsymmetric Macdonald polynomials and standard bases and dual standard bases of maximal parabolic modules of affine Hecke algebras. Along the way we prove a (weak) polynomiality result for…

We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…

In this paper we derive the bi-orthogonality relations, diagonal term evaluations and evaluation formulas for the non-symmetric Koornwinder polynomials. For the derivation we use certain representations of the (double) affine Hecke algebra…

We give a full classification, in terms of periodic skew diagrams, of irreducible semisimple modules in category O for the degenerate double affine Hecke algebra of type A which can be realized as submodules of Verma modules.

In the theory of combinatorial algebras, there is a sequence of embeddings between Kleene's second model, van Oosten's model, and Scott's graph model. We prove that none of these embeddings can be reversed. We also prove nonembedding…