Let G be a compact connected Lie group and let H be a subgroup fixed by an involution. A classical result assures that the Hℂ-action on the flag variety F of G admits a finite number of orbits. In ...this article we propose a formula for the branching coefficients of the symmetric pair (G,H) that is parametrized by Hℂ∖F.
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.
We compute the CM volume, that is the degree of the descended CM line bundle on the coarse moduli space in two cases: on the Fano
K
-moduli space of quartic del Pezzo in any dimension, and on the
K
...-moduli space of the log Fano hyperplane arrangements of dimension one and two. Furthermore, we relate these volumes to the Weil–Petersson volumes by extending the notion of Weil–Petersson metric in the log case.
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