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We define a new notion of cuspidality for representations of GL n over a finite quotient o k of the ring of integers o of a non-Archimedean local field F using geometric and infinitesimal induction functors, which involve automorphism groups G λ of torsion o-modules. When n is a prime, we show that this notion of cuspidality is equivalent to strong… (More)

We introduce a new statistic on the hyperoctahedral groups (Coxeter groups of type B), and give a conjectural formula for its signed distributions over arbitrary descent classes. The statistic is analogous to the classical Coxeter length function, and features a parity condition. For descent classes which are singletons the conjectured formula gives the… (More)

Lusztig has given a construction of certain representations of re-ductive groups over finite local principal ideal rings of characteristic p, extending the construction of Deligne and Lusztig of representations of reductive groups over finite fields. We generalize Lusztig's results to reductive groups over arbitrary finite local rings. This generalization… (More)

We define a new notion of cuspidality for representations of GL n over a finite quotient o k of the ring of integers o of a non-Archimedean local field F using geometric and infinitesimal induction functors, which involve automorphism groups G λ of torsion o-modules. When n is a prime, we show that this notion of cuspidality is equivalent to strong… (More)

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