Left Demazure–Lusztig Operators on Equivariant (Quantum) Cohomology and K-Theory
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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.
2016 ◽
Vol 152
(12)
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pp. 2603-2625
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1990 ◽
Vol 20
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pp. 637-650
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2009 ◽
Vol 148
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pp. 501-538
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2004 ◽
Vol 185
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pp. 347-369
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2007 ◽
Vol 09
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pp. 1-20
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