scholarly journals Chevalley formula for anti-dominant weights in the equivariant K-theory of semi-infinite flag manifolds

2021 ◽  
Vol 387 ◽  
pp. 107828
Author(s):  
Satoshi Naito ◽  
Daniel Orr ◽  
Daisuke Sagaki
Keyword(s):  
Flag Manifolds ◽  
Dominant Weights ◽  
K Theory

scholarly journals Quantum K-Theory of Grassmannians and Non-Abelian Localization

2021 ◽  
Author(s):  
Alexander Givental ◽  
◽  
Xiaohan Yan ◽  
Keyword(s):  
Finite Difference ◽  
Hypergeometric Series ◽  
Rational Curves ◽  
Flag Manifolds ◽  
Difference Operators ◽  
Jackson Type ◽  
Quiver Varieties ◽  
K Theory

In the example of complex grassmannians, we demonstrate various techniques available for computing genus-0 K-theoretic GW-invariants of flag manifolds and more general quiver varieties. In particular, we address explicit reconstruction of all such invariants using finite-difference operators, the role of the q-hypergeometric series arising in the context of quasimap compactifications of spaces of rational curves in such varieties, the theory of twisted GW-invariants including level structures, as well as the Jackson-type integrals playing the role of equivariant K-theoretic mirrors.

scholarly journals Left Demazure–Lusztig Operators on Equivariant (Quantum) Cohomology and K-Theory

2021 ◽  
Author(s):  
Leonardo C Mihalcea ◽  
Hiroshi Naruse ◽  
Changjian Su
Keyword(s):  
Divided Difference ◽  
Quantum Cohomology ◽  
Flag Manifold ◽  
Leibniz Rule ◽  
Flag Manifolds ◽  
Difference Operators ◽  
Left Multiplication ◽  
Schubert Classes ◽  
Left And Right ◽  
K Theory

Abstract We study the Demazure–Lusztig operators induced by the left multiplication on partial flag manifolds $G/P$. We prove that they generate the Chern–Schwartz–MacPherson classes of Schubert cells (in equivariant cohomology), respectively their motivic Chern classes (in equivariant K-theory), in any partial flag manifold. Along the way, we advertise many properties of the left and right divided difference operators in cohomology and K-theory and their actions on Schubert classes. We apply this to construct left divided difference operators in equivariant quantum cohomology, and equivariant quantum K-theory, generating Schubert classes and satisfying a Leibniz rule compatible with the quantum product.

scholarly journals Equivariant $K$ -theory of semi-infinite flag manifolds and the Pieri–Chevalley formula

2020 ◽  
Vol 169 (13) ◽  
pp. 2421-2500
Author(s):  
Syu Kato ◽  
Satoshi Naito ◽  
Daisuke Sagaki
Keyword(s):  
Flag Manifolds ◽  
K Theory

Stable Parallelizability of Partially Oriented Flag Manifolds II

1997 ◽  
Vol 49 (6) ◽  
pp. 1323-1339 ◽  
Author(s):  
Parameswaran Sankaran ◽  
Peter Zvengrowski
Keyword(s):  
Flag Manifolds ◽  
Dimensional Manifold ◽  
K Theory

AbstractIn the first paper with the same title the authors were able to determine all partially oriented flag manifolds that are stably parallelizable or parallelizable, apart from four infinite families that were undecided. Here, using more delicate techniques (mainly K-theory),we settle these previously undecided families and show that none of the manifolds in them is stably parallelizable, apart from one 30-dimensional manifold which still remains undecided.

scholarly journals Equivariant K-theory of quaternionic flag manifolds

2009 ◽  
Vol 4 (3) ◽  
pp. 537-557
Author(s):  
Augustin-Liviu Mare ◽  
Matthieu Willems
Keyword(s):  
Group Action ◽  
Maximal Torus ◽  
Flag Variety ◽  
Flag Manifolds ◽  
Skew Field ◽  
K Theory ◽  
Complex Flag

AbstractWe consider the manifold Fln(ℍ) = Sp(n)/Sp(1)n of all complete flags in ℍn, where ℍ is the skew-field of quaternions. We study its equivariant complex K-theory rings with respect to the action of two groups: Sp(1)n and a certain canonical subgroup T = (S1)n (a maximal torus). For the first group action we obtain a Goresky-Kottwitz-MacPherson type description. For the second one, we describe the ring KT(Fln(ℍ)) as a subring of KT(Sp(n)/T). This ring is well known, since Sp(n)/T is a complex flag variety.

An Introduction to K-Theory for C*-Algebras

2000 ◽  
Author(s):  
M. Rørdam ◽  
F. Larsen ◽  
N. Laustsen
Keyword(s):  
C Algebras ◽  
K Theory
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