Carlos A. M. André

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math.RT2024

Schur-Weyl dualities for the rook monoid: an approach via Schur algebras

Carlos A. M. André, Inês Legatheaux Martins

The rook monoid, also known as the symmetric inverse monoid, is the archetypal structure when it comes to extend the principle of symmetry. In this paper, we establish a Schur-Weyl…

math.RT2024

Shintani descent for standard supercharacters of algebra groups

Carlos A. M. André, Ana L. Branco Correia, João Dias

Let $A (q)$ be a finite-dimensional nilpotent algebra over a finite field $F_{q}$ with $q$ elements, and let $G (q) = 1 + A (q)$ . On the other hand, let $\B…

math.RT2024

Smooth representations of involutive algebra groups over non-archimedean local fields

Carlos A. M. André, João Dias

An algebra group over a field $F$ is a group of the form $G = 1 + J$ where $J$ is a finite-dimensional nilpotent associative $F$ -algebra. A theorem of M. Boyarchenko asserts that, in…