Quantum cohomology of infinite dimensional flag manifolds

2002 ◽  
pp. 199-209 ◽  
Author(s):  
Takashi Otofuji
Keyword(s):  
Quantum Cohomology ◽  
Flag Manifolds ◽  
Infinite Dimensional

scholarly journals GLSMs for exotic Grassmannians

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Wei Gu ◽  
Eric Sharpe ◽  
Hao Zou
Keyword(s):  
Global Symmetries ◽  
Sigma Models ◽  
Quantum Cohomology ◽  
Flag Manifolds ◽  
Coulomb Branch ◽  
Linear Sigma Models ◽  
Symplectic Grassmannians ◽  
Orthogonal Grassmannians

Abstract In this paper we explore nonabelian gauged linear sigma models (GLSMs) for symplectic and orthogonal Grassmannians and flag manifolds, checking e.g. global symmetries, Witten indices, and Calabi-Yau conditions, following up a proposal in the math community. For symplectic Grassmannians, we check that Coulomb branch vacua of the GLSM are consistent with ordinary and equivariant quantum cohomology of the space.

scholarly journals Quantum cohomology of partial flag manifolds $$F_{n_1 } \ldots _{n_k }$$

1995 ◽  
Vol 170 (3) ◽  
pp. 503-528 ◽  
Author(s):  
Alexander Astashkevich ◽  
Vladimir Sadov
Keyword(s):  
Quantum Cohomology ◽  
Flag Manifolds

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 A Murgnahan-Nakayama rule for Schubert polynomials

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Andrew Morrison
Keyword(s):  
Quantum Cohomology ◽  
Chern Character ◽  
Intersection Theory ◽  
Flag Manifolds ◽  
Nous Obtenons ◽  
Schubert Polynomial ◽  
Power Sum ◽  
Schubert Polynomials ◽  
Small Quantum ◽  
International Audience

International audience We expose a rule for multiplying a general Schubert polynomial with a power sum polynomial in $k$ variables. A signed sum over cyclic permutations replaces the signed sum over rim hooks in the classical Murgnahan-Nakayama rule. In the intersection theory of flag manifolds this computes all intersections of Schubert cycles with tautological classes coming from the Chern character. We also discuss extensions of this rule to small quantum cohomology. Nous écrivons une formule pour multiplier les polynômes de Schubert avec les sommes de Newton. Une somme signée de permutations cycliques remplace la somme signée de rubans dans la formule classique de Murgnahan-Nakayama. Nous obtenons donc des relations dans l’anneau de Chow de la variété de drapeaux. Nous discutons également des extensions de cette formule en cohomologie quantique.

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