scholarly journals On special pieces, the Springer correspondence, and unipotent characters

2008 ◽  
Vol 130 (5) ◽  
pp. 1399-1425 ◽  
Author(s):  
Pramod N. Achar ◽  
Daniel S. Sage
Keyword(s):  
Springer Correspondence

Characters of Depth-Zero, Supercuspidal Representations of the Rank-2 Symplectic Group

2000 ◽  
Vol 52 (2) ◽  
pp. 306-331 ◽  
Author(s):  
Clifton Cunningham
Keyword(s):  
Lie Algebras ◽  
Symplectic Group ◽  
Orbital Integrals ◽  
Finite Linear Combination ◽  
Supercuspidal Representations ◽  
Rank 2 ◽  
The Fourier Transform ◽  
The Stability ◽  
Springer Correspondence ◽  
Finite Linear

AbstractThis paper expresses the character of certain depth-zero supercuspidal representations of the rank-2 symplectic group as the Fourier transform of a finite linear combination of regular elliptic orbital integrals—an expression which is ideally suited for the study of the stability of those characters. Building on work of F. Murnaghan, our proof involves Lusztig’s Generalised Springer Correspondence in a fundamental way, and also makes use of some results on elliptic orbital integrals proved elsewhere by the author using Moy-Prasad filtrations of p-adic Lie algebras. Two applications of the main result are considered toward the end of the paper.

scholarly journals Character sheaves and generalized Springer correspondence

2003 ◽  
Vol 170 ◽  
pp. 47-72 ◽  
Author(s):  
Anne-Marie Aubert
Keyword(s):  
Finite Field ◽  
Algebraic Group ◽  
Algebraic Closure ◽  
Reductive Algebraic Group ◽  
Good For ◽  
Character Sheaves ◽  
Springer Correspondence

AbstractLetGbe a connected reductive algebraic group over an algebraic closure of a finite field of characteristicp. Under the assumption thatpis good forG, we prove that for each character sheafAonGwhich has nonzero restriction to the unipotent variety ofG, there exists a unipotent classCAcanonically attached toA, such thatAhas non-zero restriction onCA, and any unipotent classCinGon whichAhas non-zero restriction has dimension strictly smaller than that ofCA.

scholarly journals Springer correspondence for the split symmetric pair in type

2018 ◽  
Vol 154 (11) ◽  
pp. 2403-2425 ◽  
Author(s):  
Tsao-Hsien Chen ◽  
Kari Vilonen ◽  
Ting Xue
Keyword(s):  
Fourier Transform ◽  
Hecke Algebras ◽  
Symmetric Groups ◽  
Irreducible Representations ◽  
Symmetric Pair ◽  
Parabolic Induction ◽  
Hessenberg Varieties ◽  
Nearby Cycle ◽  
Springer Correspondence

In this paper we establish Springer correspondence for the symmetric pair $(\text{SL}(N),\text{SO}(N))$ using Fourier transform, parabolic induction functor, and a nearby cycle sheaf construction. As an application of our results we see that the cohomology of Hessenberg varieties can be expressed in terms of irreducible representations of Hecke algebras of symmetric groups at $q=-1$. Conversely, we see that the irreducible representations of Hecke algebras of symmetric groups at $q=-1$ arise in geometry.

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