scholarly journals Multiplicative formulas in Schubert calculus and quiver representation

2011 ◽  
Vol 22 (1-2) ◽  
pp. 87-102 ◽  
Author(s):  
N. Ressayre
Keyword(s):  
Schubert Calculus ◽  
Quiver Representation

scholarly journals Equivariant -theory of Grassmannians II: the Knutson–Vakil conjecture

2017 ◽  
Vol 153 (4) ◽  
pp. 667-677 ◽  
Author(s):  
Oliver Pechenik ◽  
Alexander Yong
Keyword(s):  
Schubert Calculus ◽  
Equivariant Theory

In 2005, Knutson–Vakil conjectured apuzzlerule for equivariant$K$-theory of Grassmannians. We resolve this conjecture. After giving a correction, we establish a modified rule by combinatorially connecting it to the authors’ recently proved tableau rule for the same Schubert calculus problem.

scholarly journals Schubert calculus and threshold polynomials of affine fusion

2000 ◽  
Vol 584 (3) ◽  
pp. 795-809 ◽  
Author(s):  
S.E. Irvine ◽  
M.A. Walton
Keyword(s):  
Schubert Calculus

scholarly journals Dynamic Pole Assignment and Schubert Calculus

1996 ◽  
Vol 34 (3) ◽  
pp. 813-832 ◽  
Author(s):  
M. S. Ravi ◽  
Joachim Rosenthal ◽  
Xiaochang Wang
Keyword(s):  
Pole Assignment ◽  
Schubert Calculus

scholarly journals Nori Motives of Curves With Modulus and Laumon 1-motives

2018 ◽  
Vol 70 (4) ◽  
pp. 868-897 ◽  
Author(s):  
Florian Ivorra ◽  
Takao Yamazaki
Keyword(s):  
Number Field ◽  
Abelian Category ◽  
Quiver Representation ◽  
Universal Category ◽  
Effective Divisors

AbstractLet k be a number field. We describe the category of Laumon 1-isomotives over k as the universal category in the sense of M. Nori associated with a quiver representation built out of smooth proper k-curves with two disjoint effective divisors and a notion of for such “curves with modulus”. This result extends and relies on a theorem of J. Ayoub and L. Barbieri-Viale that describes Deligne's category of 1-isomotives in terms of Nori's Abelian category of motives.

scholarly journals The elliptic Weyl character formula

2014 ◽  
Vol 150 (7) ◽  
pp. 1196-1234 ◽  
Author(s):  
Nora Ganter
Keyword(s):  
Line Bundle ◽  
Lie Groups ◽  
Theoretical Framework ◽  
Flag Variety ◽  
Schubert Calculus ◽  
Character Formula ◽  
Elliptic Cohomology ◽  
Image Position ◽  
Weyl Character Formula

AbstractWe calculate equivariant elliptic cohomology of the partial flag variety$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G/H$, where$H\subseteq G$are compact connected Lie groups of equal rank. We identify the${\rm RO}(G)$-graded coefficients${\mathcal{E}} ll_G^*$as powers of Looijenga’s line bundle and prove that transfer along the map$$\begin{equation*} \pi \,{:}\,G/H\longrightarrow {\rm pt} \end{equation*}$$is calculated by the Weyl–Kac character formula. Treating ordinary cohomology,$K$-theory and elliptic cohomology in parallel, this paper organizes the theoretical framework for the elliptic Schubert calculus of [N. Ganter and A. Ram,Elliptic Schubert calculus, in preparation].

scholarly journals Multiplicity-Free Schubert Calculus

2010 ◽  
Vol 53 (1) ◽  
pp. 171-186 ◽  
Author(s):  
Hugh Thomas ◽  
Alexander Yong
Keyword(s):  
Algebraic Geometry ◽  
Schubert Calculus ◽  
Chow Ring ◽  
Free Products ◽  
Linear Basis ◽  
Combinatorial Classification ◽  
Schubert Classes ◽  
Multiplicity Free

AbstractMultiplicity-free algebraic geometry is the study of subvarieties Y ⊆ X with the “smallest invariants” as witnessed by a multiplicity-free Chow ring decomposition of [Y] ∈ A*(X) into a predetermined linear basis.This paper concerns the case of Richardson subvarieties of the Grassmannian in terms of the Schubert basis. We give a nonrecursive combinatorial classification of multiplicity-free Richardson varieties, i.e., we classify multiplicity-free products of Schubert classes. This answers a question of W. Fulton.

scholarly journals Towards generalizing Schubert calculus in the symplectic category

2009 ◽  
Vol 7 (4) ◽  
pp. 449-473 ◽  
Author(s):  
Rebecca F. Goldin ◽  
Susan Tolman
Keyword(s):  
Schubert Calculus
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