A Comparison of Two Complexes

2016/03/12 by Kim, Dongkwan · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1603.03845

Abstract

In this paper we prove the conjecture of Lusztig in "Generic character sheaves on groups over k[ε]/(ε^r)." Given a reductive group over \mathbbF_q for some r≥ 2, there is a notion of a character sheaf defined in "Character sheaves and generalizations" by Lusztig. On the other hand, there is also a geometric analogue of the character constructed by Gérardin. The conjecture states that the two constructions are equivalent, which Lusztig also proved for r=2, 3, 4. Here we generalize his method to prove this conjecture for general r. As a corollary we prove that the characters derived from these two complexes are equal.

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