Structure constants for K-theory of Grassmannians, revisited
نویسندگان
چکیده
منابع مشابه
Quantum K-theory of Grassmannians
We show that (equivariant) K-theoretic 3-point Gromov-Witten invariants of genus zero on a Grassmann variety are equal to triple intersections computed in the ordinary (equivariant) K-theory of a two-step flag manifold, thus generalizing an earlier result of Buch, Kresch, and Tamvakis. In the process we show that the Gromov-Witten variety of curves passing through 3 general points is irreducibl...
متن کاملA Littlewood-richardson Rule for the K-theory of Grassmannians
We prove an explicit combinatorial formula for the structure constants of the Grothendieck ring of a Grassmann variety with respect to its basis of Schubert structure sheaves. We furthermore relate K-theory of Grassmannians to a bialgebra of stable Grothendieck polynomials, which is a K-theory parallel of the ring of symmetric functions.
متن کاملPieri Rules for the K-theory of Cominuscule Grassmannians
We prove Pieri formulas for the multiplication with special Schubert classes in the K-theory of all cominuscule Grassmannians. For Grassmannians of type A this gives a new proof of a formula of Lenart. Our formula is new for Lagrangian Grassmannians, and for orthogonal Grassmannians it proves a special case of a conjectural Littlewood-Richardson rule of Thomas and Yong. Recent work of Thomas an...
متن کاملCombinatorics of the K-theory of Affine Grassmannians
We introduce a family of tableaux that simultaneously generalizes the tableaux used to characterize Grothendieck polynomials and k-Schur functions. We prove that the polynomials drawn from these tableaux are the affine Grothendieck polynomials and k-K-Schur functions – Schubert representatives for the K-theory of affine Grassmannians and their dual in the nil Hecke ring. We prove a number of co...
متن کاملNotes on the K-theory of Complex Grassmannians
generators. Our goal is to make this description more concrete. Note that G(k, n) = U(n)/(U(k)×U(n− k)) = St(k, n)/U(k) is the quotient by U(k) of the complex Stiefel manifold St(k, n) of partial orthonormal k-frames in C. Thus any finite-dimensional representation ρ : U(k) −→ GL(W ) of U(k) gives rise to the natural vector bundle St(k, n)×ρ W −→ G(k, n), where St(k, n) −→ G(k, n) is viewed as ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2016
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2016.06.016