arXiv subjects
Publications and source records attributed to Masoud Kamgarpour.
For certain characters of the compact torus of a reductive $p$-adic group, which we call strongly parabolic characters, we prove Satake-type isomorphisms. Our results generalize those of Satake, Howe, Bushnell and Kutzko, and Roche.
In geometric representation theory, one often wishes to describe representations realized on spaces of invariant functions as trace functions of equivariant perverse sheaves. In the case of principal series representations of a connected split reductive group G over a local field, there is a description of families of these representations realized on spaces of functions on G invariant under the translation action of the Iwahori subgroup, or a suitable smaller compact open subgroup, studied by Howe, Bushnell and Kutzko, Roche, and others. In this paper, we construct categories of perverse sheaves whose traces recover the families associated to regular characters of T(F_q[[t]]), and prove conjectures of Drinfeld on their structure. We also propose conjectures on the geometrization of families associated to more general characters.
We define the $p$-adic trace of certain rank-one local systems on the multiplicative group over $p$-adic numbers, using Sekiguchi and Suwa's unification of Kummer and Artin-Schrier-Witt theories. Our main observation is that, for every non-negative integer $n$, the $p$-adic trace defines an isomorphism of abelian groups between local systems whose order divides $(p-1)p^n$ and $\ell$-adic characters of the multiplicative group of $p$-adic integers of depth less than or equal to $n$.
We sharpen the orbit method for finite groups of small nilpotence class by associating representations to functionals on the corresponding Lie rings. This amounts to describing compatible intertwiners between representations parameterized by an additional choice of polarization. Our construction is motivated by the theory of the linearized Weil representation of the symplectic group. In particular, we provide generalizations of the Maslov index and the determinant functor to the context of finite abelian groups.
The representation dimension of a finite group G is the smallest positive integer m for which there exists an embedding of G in GL_m(C). In this paper we find the largest value of representation dimensions, as Granges over all groups of order p^n, for a fixed prime p and a fixed exponent n greater than zero.
Let G be a connected algebraic group and let [G,G] be its commutator subgroup. We prove a conjecture of Drinfeld about the existence of a connected etale group cover H of [G,G], characterized by the following properties: every central extension of G, by a finite etale group scheme, splits over H, and the commutator map of G lifts to H. We prove, moreover, that the quotient stack of G by the natural action of H is the universal Deligne-Mumford Picard stack to which G maps.