TY - JOUR

T1 - A comparison of two complexes

AU - Kim, Dongkwan

N1 - Publisher Copyright:
© 2018 Elsevier Inc.

PY - 2018/11/15

Y1 - 2018/11/15

N2 - We prove the conjecture of Lusztig in [5, Section 4]. Given a reductive group over Fq‾[ε]/(εr) for some r≥2, there is a notion of a character sheaf defined in [4, Section 8]. On the other hand, there is also a geometric analogue of the character constructed by Gérardin [2]. The conjecture in [5, Section 4] 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.

AB - We prove the conjecture of Lusztig in [5, Section 4]. Given a reductive group over Fq‾[ε]/(εr) for some r≥2, there is a notion of a character sheaf defined in [4, Section 8]. On the other hand, there is also a geometric analogue of the character constructed by Gérardin [2]. The conjecture in [5, Section 4] 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.

KW - Character sheaf

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U2 - 10.1016/j.jalgebra.2018.07.038

DO - 10.1016/j.jalgebra.2018.07.038

M3 - Article

AN - SCOPUS:85052304046

SN - 0021-8693

VL - 514

SP - 76

EP - 98

JO - Journal of Algebra

JF - Journal of Algebra

ER -