scholarly journals Quotients of flag varieties by a maximal torus

2000 ◽  
Vol 234 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Elisabetta Strickland
Keyword(s):  
Maximal Torus ◽  
Flag Varieties

scholarly journals A FILTRATION ON EQUIVARIANT BOREL–MOORE HOMOLOGY

2019 ◽  
Vol 7 ◽  
Author(s):  
ARAM BINGHAM ◽  
MAHIR BILEN CAN ◽  
YILDIRAY OZAN
Keyword(s):  
Fixed Point ◽  
Maximal Torus ◽  
Flag Varieties ◽  
Direct Sum ◽  
Equivariant Embedding ◽  
Graded Module ◽  
Homogeneous Variety

Let $G/H$ be a homogeneous variety and let $X$ be a $G$ -equivariant embedding of $G/H$ such that the number of $G$ -orbits in $X$ is finite. We show that the equivariant Borel–Moore homology of $X$ has a filtration with associated graded module the direct sum of the equivariant Borel–Moore homologies of the $G$ -orbits. If $T$ is a maximal torus of $G$ such that each $G$ -orbit has a $T$ -fixed point, then the equivariant filtration descends to give a filtration on the ordinary Borel–Moore homology of $X$ . We apply our findings to certain wonderful compactifications as well as to double flag varieties.

Tropical flag varieties

2021 ◽  
Vol 384 ◽  
pp. 107695
Author(s):  
Madeline Brandt ◽  
Christopher Eur ◽  
Leon Zhang
Keyword(s):  
Flag Varieties

scholarly journals Projective normality of torus quotients of flag varieties

2020 ◽  
Vol 224 (10) ◽  
pp. 106389
Author(s):  
Arpita Nayek ◽  
S.K. Pattanayak ◽  
Shivang Jindal
Keyword(s):  
Flag Varieties ◽  
Projective Normality

scholarly journals A decomposition formula for representations

1987 ◽  
Vol 107 ◽  
pp. 63-68 ◽  
Author(s):  
George Kempf
Keyword(s):  
Irreducible Representation ◽  
General Formula ◽  
Parabolic Subgroup ◽  
Characteristic Zero ◽  
Maximal Torus ◽  
Reductive Group ◽  
Irreducible Representations ◽  
Levi Subgroup ◽  
Know How ◽  
Decomposition Formula

Let H be the Levi subgroup of a parabolic subgroup of a split reductive group G. In characteristic zero, an irreducible representation V of G decomposes when restricted to H into a sum V = ⊕mαWα where the Wα’s are distinct irreducible representations of H. We will give a formula for the multiplicities mα. When H is the maximal torus, this formula is Weyl’s character formula. In theory one may deduce the general formula from Weyl’s result but I do not know how to do this.

scholarly journals Euler characteristics in the quantum K-theory of flag varieties

2020 ◽  
Vol 26 (2) ◽  
Author(s):  
Anders S. Buch ◽  
Sjuvon Chung ◽  
Changzheng Li ◽  
Leonardo C. Mihalcea
Keyword(s):  
Flag Varieties ◽  
Euler Characteristics ◽  
K Theory

scholarly journals Orthogonal groups containing a given maximal torus

2003 ◽  
Vol 266 (1) ◽  
pp. 87-101 ◽  
Author(s):  
Rosali Brusamarello ◽  
Pascale Chuard-Koulmann ◽  
Jorge Morales
Keyword(s):  
Maximal Torus ◽  
Orthogonal Groups

Chow groups of some generically twisted flag varieties

2017 ◽  
Vol 2 (2) ◽  
pp. 341-356 ◽  
Author(s):  
Nikita Karpenko
Keyword(s):  
Chow Groups ◽  
Flag 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.

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