ﻻ يوجد ملخص باللغة العربية
We introduce an infinite-dimensional $p$-adic affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by the fact that the group does not act on the phase space. However it is possible to define its action on some classes of functions.
We begin this paper by reviewing the Langlands correspondence for unipotent representations of the exceptional group of type $G_2$ over a $p$-adic field $F$ and present it in an explicit form. Then we compute all ABV-packets, as defined in [CFM+21] f
The general construction of frames of p-adic wavelets is described. We consider the orbit of a mean zero generic locally constant function with compact support (mean zero test function) with respect to the action of the p-adic affine group and show t
Motivated by physical and topological applications, we study representations of the group $mathcal{LB}_3$ of motions of $3$ unlinked oriented circles in $mathbb{R}^3$. Our point of view is to regard the three strand braid group $mathcal{B}_3$ as a su
We prove the twisted Whittaker category on the affine flag variety and the category of representations of the mixed quantum group are equivalent.
Inspired by the work [Ra1], we directly give a complete classification of irreducible calibrated representations of affine Yokonuma-Hecke algebras $widehat{Y}_{r,n}(q)$ over $mathbb{C},$ which are indexed by $r$-tuples of placed skew shapes. We then