Robin J. Sroka

Double Steinberg coinvariants for special linear groups

For a field $F$ we study the coinvariants for the $SL_n(F)$-action on the double Steinberg module $St_n(F) \otimes St_n(F)$ and show they have a rich algebraic structure: for $n = 2$ it is the Grothendieck-Witt group of $F$, and for all $n$ they assemble to a graded nonunital $\mathbb{Z}[F^\times]$-algebra, whose ratio...