Functorality of the gamma filtration and computations for some twisted flag varieties

AbstractFor the Grothendieck group of a split simple linear algebraic group, the twisted γ-filtration provides a useful tool for constructing torsion elements in -rings of twisted flag varieties. In this paper, we construct a non-trivial torsion element in the γ-ring of a complete flag variety twisted by means of a PGO-torsor. This generalizes the construction in the HSpin case previously obtained by Zainoulline.

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Twisted gamma filtration of a linear algebraic group

Compositio Mathematica ◽

10.1112/s0010437x11007494 ◽

2012 ◽

Vol 148 (5) ◽

pp. 1645-1654 ◽

Cited By ~ 4

Author(s):

Kirill Zainoulline

Keyword(s):

Algebraic Group ◽

Linear Algebraic Group ◽

Flag Varieties ◽

Gamma Filtration

AbstractIn the present paper we introduce and study the twisted γ-filtration on K0(Gs), where Gs is a split simple linear algebraic group over a field k of characteristic prime to the order of the center of Gs. We apply this filtration to construct nontrivial torsion elements in γ-rings of twisted flag varieties.

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Tropical flag varieties

Advances in Mathematics ◽

10.1016/j.aim.2021.107695 ◽

2021 ◽

Vol 384 ◽

pp. 107695

Author(s):

Madeline Brandt ◽

Christopher Eur ◽

Leon Zhang

Keyword(s):

Flag Varieties

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Projective normality of torus quotients of flag varieties

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2020.106389 ◽

2020 ◽

Vol 224 (10) ◽

pp. 106389

Author(s):

Arpita Nayek ◽

S.K. Pattanayak ◽

Shivang Jindal

Keyword(s):

Flag Varieties ◽

Projective Normality

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Euler characteristics in the quantum K-theory of flag varieties

Selecta Mathematica ◽

10.1007/s00029-020-00557-7 ◽

2020 ◽

Vol 26 (2) ◽

Author(s):

Anders S. Buch ◽

Sjuvon Chung ◽

Changzheng Li ◽

Leonardo C. Mihalcea

Keyword(s):

Flag Varieties ◽

Euler Characteristics ◽

K Theory

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Chow groups of some generically twisted flag varieties

Annals of K-Theory ◽

10.2140/akt.2017.2.341 ◽

2017 ◽

Vol 2 (2) ◽

pp. 341-356 ◽

Cited By ~ 5

Author(s):

Nikita Karpenko

Keyword(s):

Chow Groups ◽

Flag Varieties

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Inversions Within Restricted Fillings of Young Tableaux

The Electronic Journal of Combinatorics ◽

10.37236/1030 ◽

2006 ◽

Vol 13 (1) ◽

Cited By ~ 3

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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