Primer on k-Schur Functions

Lam, Thomas; Lapointe, Luc; Morse, Jennifer; Schilling, Anne; Shimozono, Mark; Zabrocki, Mike

doi:10.1007/978-1-4939-0682-6_2

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K-k-schur Functions1

Proof (⇐) Consider An α-Factorization W1

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“…has recently been proven in [AB09] and in [LLMS09b]. The path to proving this result that is taken in [LLMS09b] proves the more refined property that…”

Section: K-k-schur Functionsmentioning

confidence: 73%

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Combinatorics of the K-theory of affine Grassmannians

Morse

2012

Advances in Mathematics

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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 combinatorial properties including Pieri rules.

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“…has recently been proven in [AB09] and in [LLMS09b]. The path to proving this result that is taken in [LLMS09b] proves the more refined property that…”

Section: K-k-schur Functionsmentioning

confidence: 73%

“…On the other hand, instead viewing affine Grothendieck polynomials as the Ktheoretic analog of dual k-Schur functions suggests that these polynomials satisfy even more refined combinatorial properties. For example, it is proven in the forthcoming paper [LLMS09b] that the coefficients in…”

Section: Proof (⇐) Consider An α-Factorization Wmentioning

confidence: 99%

Combinatorics of the K-theory of affine Grassmannians

Morse

2012

Advances in Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

Primer on k-Schur Functions

Cited by 1 publication

References 74 publications

Combinatorics of the K-theory of affine Grassmannians

Combinatorics of the K-theory of affine Grassmannians

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