Related papers: Extensions of representations of p-adic groups
Some question about representations of $p$-adic groups are discussed.
In this note, we verify that several fundamental results from the theory of representations of reductive $p$-adic groups, extend to finite central extensions of these groups.
We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…
We perform the computations necessary to establish a multiplicity one statement for the irreducible representations of a finite spin group which in turn yields the classification of irreducible representations of finite spin groups. (The…
A complete list of one dimensional groups definable in the p-adic numbers is given, up to a finite index subroup and a quotient by a finite subgroup.
We investigate the rate of growth of the function of n which counts the number of complex irreducible representations of a fixed group of degree less than or equal to n. The emphasis is on linear groups, especially compact real and p-adic…
We give a classification of irreducible admissible modulo $p$ representations of a split $p$-adic reductive group in terms of supersingular representations. This is a generalization of a theorem of Herzig.
We give a method to construct new self-adjoint representations of the braid group. In particular, we give a family of irreducible self-adjoint representations of dimension arbitrarily large. Moreover we give sufficient conditions for a…
We study beta-extensions in a p-adic classical group and we produce a relation between some beta-extensions by means of a Weil representation. We apply this to the study of reducibility points of some parabolically induced representations.
For the ring R of integers of a ramified extension of the field of p-adic numbers and a cyclic group G of prime order p we study the extensions of the additive groups of R-representations modules of G by the group G.
We prove that there is a one-one correspondence between sets of irreducible representations of a polyadic group and its Post's cover. Using this correspondence, we generalize some well-known properties of irreducible characters in finite…
We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…
We determine the finite groups whose real irreducible representations have different degrees.
Let $F$ be a local field over $\mathbf{Q}_p$ or $\mathbf{F}_p((t))$, and let $D$ be a central simple division algebra over $F$ of degree $d$. In the $p$-adic case, we assume $p>de+1$ where $e$ is the ramification degree over $\mathbf{Q}_p$;…
In this short note, we compute higher extension groups for all irreducible representations and deduce the multiplicity formula for finite length representations in triple product case.
We obtain a description of the irreducible representation algebra of the alternating group of degree four over the ring of 2-adic integers.
In this note we produce examples of converging sequences of Galois representations, and study some of their properties. Some of the results here are used in the preprint math.NT/0210296.
We calculate the extension groups between simple modules of pro-$p$-Iwahori Hecke algebras.
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…
We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…