scholarly journals Hessenberg varieties, intersections of quadrics, and the Springer correspondence

2020 ◽  
Vol 373 (4) ◽  
pp. 2427-2461
Author(s):  
Tsao-Hsien Chen ◽  
Kari Vilonen ◽  
Ting Xue
Keyword(s):  
Hessenberg Varieties ◽  
Springer Correspondence

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.

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

scholarly journals The connectedness of Hessenberg varieties

2015 ◽  
Vol 437 ◽  
pp. 34-43 ◽  
Author(s):  
Martha Precup
Keyword(s):  
Hessenberg Varieties

scholarly journals Geometry of Hessenberg varieties with applications to Newton–Okounkov bodies

2018 ◽  
Vol 24 (3) ◽  
pp. 2129-2163 ◽  
Author(s):  
Hiraku Abe ◽  
Lauren DeDieu ◽  
Federico Galetto ◽  
Megumi Harada
Keyword(s):  
Hessenberg Varieties

scholarly journals Inversions Within Restricted Fillings of Young Tableaux

10.37236/1030 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Sarah Iveson
Keyword(s):  
Upper Bound ◽  
Exact Expression ◽  
Flag Varieties ◽  
Young Tableaux ◽  
Geometric Properties ◽  
Number Of Components ◽  
Hessenberg Varieties ◽  
Special Cases

In this paper we study inversions within restricted fillings of Young tableaux. These restricted fillings are of interest because they describe geometric properties of certain subvarieties, called Hessenberg varieties, of flag varieties. We give answers and partial answers to some conjectures posed by Tymoczko. In particular, we find the number of components of these varieties, give an upper bound on the dimensions of the varieties, and give an exact expression for the dimension in some special cases. The proofs given are all combinatorial.

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 A filtration on the cohomology rings of regular nilpotent Hessenberg varieties

2020 ◽  
Author(s):  
Megumi Harada ◽  
Tatsuya Horiguchi ◽  
Satoshi Murai ◽  
Martha Precup ◽  
Julianna Tymoczko
Keyword(s):  
Cohomology Rings ◽  
Hessenberg Varieties
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