In this article we work with the degenerate affine Hecke algebra Hl corresponding to the general linear group GLl over a local non-Archimedean field. This algebra was introduced by V.Drinfeld in [D], see also [L]. The complex associative algebra Hl is generated by the symmetric group algebra CSl and by the pairwise commuting elements x1 , . . . , xl with the cross relations for p = 1 , . . . , ...

Let $F$ be a non-Archimedean locally compact field‎. ‎Let $sigma$ and $tau$ be finite-dimensional representations of the Weil-Deligne group of $F$‎. ‎We give strong upper and lower bounds for the Artin and Swan exponents of $sigmaotimestau$ in terms of those of $sigma$ and $tau$‎. ‎We give a different lower bound in terms of $sigmaotimeschecksigma$ and $tauotimeschecktau$‎. ‎Using the Langlands...

Let G be a split reductive algebraic group over a non-archimedean local field. We study the representation theory of a central extension G̃ of G by a cyclic group of order n, under some mild tameness assumptions on n. In particular, we focus our attention on the development of the theory of principal series representations for G̃ and its applications to the study of Hecke algebras via a Satake is...

This paper concerns the theory of intuitionistic fuzzy sets according to Atanassov. If triangular norms, especially nonstrict Archimedean ones, are used, we propose a revision and a flexibilizing generalization of some fundamental notions and constructions of that theory. Its application to group decision making is outlined.

It is known that a Mumford curve of genus g / ∈ {5, 6, 7, 8} over a non-archimedean valued field of characteristic p > 0 has at most 2 √ g( √ g+1) automorphisms. In this note, the unique family of curves which attains this bound, and their automorphism group are determined.

Let G be a reductive group over a non-Archimedean local field. For two tempered smooth representations, it makes no difference for the Ext-groups whether we work in the category of tempered smooth representations of G or of all smooth representations of G. Similar results hold for certain discrete groups. We explain the basic ideas from functional analysis and geometric group theory that are ne...

In this paper, we compute the Hecke action of a certain test function on space an unramified principal series connected reductive group over non-archimedean local field. The key our computation is theory Iwahori–Hecke algebra. As application, obtain new expression L-functions representations.

This paper studies several concepts about subgroups of automorphisms of linearly ordered relational structures. In particular, it focuses on conditions that are equivalent to the translations (automorphisms with no fixed points plus the identity) forming a homogeneous, Archimedean ordered group under the asymptotic order. For the automorphisms of an ordered relational structure, these propertie...

If there is an order-preserving group isomorphism from a directed abelian group G with a finitely generated positive cone G+ onto a simplicial group, then G is called a semisimplicial group. By factoring out the torsion subgroup of a unital group having a finite unit interval, one obtains a semisimplicial unital group. We exhibit a representation for the base-normed space associated with a semi...