| Résume | In this talk I will discuss our joint work with Emmanuel Letellier on
extending Ennola duality to a larger context. Originally, Ennola
duality was the observation by Ennola (later proved by Lusztig and
Srinivasan) that the irreducible characters of the unitary group U_n
over a finite field are essentially obtained from those of GL_n by
changing q to -q in their polynomial terms.
One may ask to what extent this duality extends to other aspects of
the representation theory of these groups, for example, to their
character rings. This appears to be indeed the case. With the
appropriate extension, we show that Ennola duality holds for the
multiplicities of tensor products of the unipotent characters of the
respective groups. This follows from a somewhat strange connection of
these multiplicities to the cohomology of certain quiver varieties.
If time permits I will also discuss a special case where numerical
evidence suggest an even stranger connection to the combinatorics of
spaces of Specht like polynomials. |
