Results 31 to 40 of about 979 (55)

Combinatorial formulas for shifted dual stable Grothendieck polynomials

Forum of Mathematics, Sigma
The K-theoretic Schur P- and Q-functions $G\hspace {-0.2mm}P_\lambda $ and $G\hspace {-0.2mm}Q_\lambda $ may be concretely defined as weight-generating functions for semistandard shifted set-valued tableaux.
Joel Lewis, Eric Marberg
doaj   +1 more source

On the K-theoretic fundamental classes of Deligne-Lusztig varieties

, 2020
In this paper we express the class of the structure sheaves of the closures of Deligne--Lusztig varieties as explicit double Grothendieck polynomials in the first Chern classes of appropriate line bundles on the ambient flag variety.
Hudson, Thomas, Peters, Dennis
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An inverse Grassmannian Littlewood–Richardson rule and extensions

Forum of Mathematics, Sigma
Chow rings of flag varieties have bases of Schubert cycles $\sigma _u $ , indexed by permutations. A major problem of algebraic combinatorics is to give a positive combinatorial formula for the structure constants of this basis.
Oliver Pechenik, Anna Weigandt
doaj   +1 more source

Smooth locus of twisted affine Schubert varieties and twisted affine Demazure modules

Forum of Mathematics, Sigma
Let ${\mathscr {G}} $ be a special parahoric group scheme of twisted type over the ring of formal power series over $\mathbb {C}$ , excluding the absolutely special case of $A^{(2)}_{2\ell }$ .
Marc Besson, Jiuzu Hong
doaj   +1 more source

Quantum K theory of Grassmannians, Wilson line operators and Schur bundles

Forum of Mathematics, Sigma
We prove a ‘Whitney’ presentation, and a ‘Coulomb branch’ presentation, for the torus equivariant quantum K theory of the Grassmann manifold $\mathrm {Gr}(k;n)$ , inspired from physics, and stated in an earlier paper.
Wei Gu, Leonardo Mihalcea, Eric Sharpe, Hao Zou   +3 more
doaj   +1 more source

A categorical action of the shifted $0$ -affine algebra

Forum of Mathematics, Sigma
We introduce a new algebra $\mathcal {U}=\dot {\mathrm {\mathbf{U}}}_{0,N}(L\mathfrak {sl}_n)$ called the shifted $0$ -affine algebra, which emerges naturally from studying coherent sheaves on n-step partial flag varieties through natural ...
You-Hung Hsu
doaj   +1 more source

The special Schubert calculus is real

, 1998
We show that the Schubert calculus of enumerative geometry is real, for special Schubert conditions. That is, for any such enumerative problem, there exist real conditions for which all the a priori complex solutions are real.Comment: 5 ...
Sottile, Frank
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A presentation of the torus-equivariant quantum K-theory ring of flag manifolds of type A, Part II: quantum double Grothendieck polynomials

Forum of Mathematics, Sigma
In our previous paper, we gave a presentation of the torus-equivariant quantum K-theory ring $QK_{H}(Fl_{n+1})$ of the (full) flag manifold $Fl_{n+1}$ of type $A_{n}$ as a quotient of a polynomial ring by an explicit ideal.
Toshiaki Maeno, Satoshi Naito, Daisuke Sagaki   +2 more
doaj   +1 more source

Vanishing of Schubert coefficients via the effective Hilbert nullstellensatz

Forum of Mathematics, Sigma
Schubert Vanishing is a problem of deciding whether Schubert coefficients are zero. Until this work it was open whether this problem is in the polynomial hierarchy ${{\mathsf {PH}}}$ .
Igor Pak, Colleen Robichaux
doaj   +1 more source

On piecewise isomorphism of some varieties

, 2011
Two quasi-projective varieties are called piecewise isomorphic if they can be stratified into pairwise isomorphic strata. We show that the m-th symmetric power $S^m(C^n)$ of the complex affine space $C^n$ is piecewise isomorphic to $C^{mn}$ and the m-th ...
Gusein-Zade, S. M., Luengo, I., Melle-Hernandez, A.   +2 more
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