Quantum K-theory of Lagrangian Grassmannian via parabolic Peterson isomorphism

2024/05/28 by Ikeda, Takeshi, Kouno, Takafumi, Nakayama, Yusuke +1
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #K-Theory and Homology (math.KT) #Primary 14M15 #Representation Theory (math.RT) #Secondary 53D45

paper · doi:10.48550/arxiv.2405.17854

Abstract

We study Schubert calculus in the torus-equivariant quantum K-ring of the Lagrangian Grassmannian LG(n). Our main tool is the K-theoretic Peterson map due to Kato. The map is from the (localized) equivariant K-homology ring K_*^T(Gr_G) of the affine Grassmannian Gr_G of the symplectic group G=Sp_2n(ℂ) to the (localized) torus-equivariant quantum K-ring QK_T(LG(n)). We determine explicitly the kernel of this map.

Related

• Quantum cohomology of the Lagrangian Grassmannian
• Quantum K-theory of G/P and K-homology of affine Grassmannian
• Relativistic Toda lattice and equivariant K-homology of affine Grassmannian
• Quantum K theory of Grassmannians, Wilson line operators, and Schur bundles
• A conjectural Peterson isomorphism in K-theory