Combinatorial Aspects of the K-Theory of Grassmannians

By Cristian Lenart. 2000

130 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3a64e5dbbf272ed4c0d347deb0b2c0a09e5d7f69

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

In Mathematical Physics

Citations in the corpus

A Littlewood-Richardson rule for theK-theory of Grassmannians (2000, methodology): “tion sµ(x) as an inﬁnite linear combination of single stable Grothendieck polynomials for partitions with the same number of columns as µ. In fact Lenart also gives an explicit formula for doing this [16]. We also need the following result of Fomin and Greene [7]. If w ∈ Sn is a permutation and λ is”
On a family of symmetric rational functions (2014, background): “The case of inhomogeneous Schur polynomials discussed in Section 8.4 bears a certain similarity to a recent work of Motegi and Sakai [15], [16] on the so-called Grothendieck polynomials, see also Lascoux and Schützenberger [11], Lenart [12] for much earlier works on those polynomials, but we were n”
A jeu de taquin theory for increasing tableaux, with applications to K-theoretic Schubert calculus (2007, methodology): “This richer environment parallels the Schur polynomial setting, as demonstrated by, e.g., [ Le00 , Bu02a, BuKrShTaYo06].”
Duality and deformations of stable Grothendieck polynomials (2016, background): “Elegant tableaux arise from nonintersecting lattice path interpretation [15] and the following determinantal formulas hold”
Combinatorial Hopf algebras and K-homology of Grassmanians (2007, methodology): “Elegant fillings were used previously in [ 10 ].”
Grothendieck classes of quiver varieties (2001, methodology): “j−1(x1,...,xn/1 i−1): GI(x1,...,xn) = det hIi+j−1(x1,...,xn/1 i−1) 1≤i,j≤n Notice that the size of this determinant depends on the number of variables. With this notation we have: Theorem 3.1 (Lenart [20]). If Iis a partition then GI(x1,...,xn) = GwI (x) = GI(x1,...,xn). Lemma 3.2. Let Iand Jbe sequ”
k-Schur Functions and Affine Schubert Calculus (2013, background): “For example, there is a combinatorial expansion of Grothendieck polynomials into Schur functions described by a family of skew tableaux [113].”
K-theory of minuscule varieties (2013, methodology): “Corollary 3.19 was proved in [28] for Grassmannians of type A and in [7, 9] for maximal orthogonal Grassmannians.”