On some factorization formulas of K-k-Schur functions

Motoki Takigiku

On some factorization formulas of K-k-Schur functions

Motoki Takigiku

Research output: Contribution to conference › Paper › peer-review

Abstract

We give some new formulas about factorizations of K-k-Schur functions g_λ^(k), analogous to the k-rectangle factorization formula s_Rt∪λ^(k)= s_Rt(k)S_λ^(k)of k-Schur functions, where λ is any k-bounded partition and Rt denotes the partition (t^k+1-t) called a k-rectangle. Although a formula of the same form does not hold for K-k-Schur functions, we can prove that g_Rdivides g_Rt∪λ^(k), and in fact more generally that g_Pdivides g_P∪λ^(k)for any multiple k-rectangles P and any k-bounded partition λ. We give the factorization formula of such g_P^(k), the explicit formulas of g_P∪λ^(k)/g_P^(k)in some cases.

Original language	English
Publication status	Published - 2006
Externally published	Yes
Event	29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017 - London, United Kingdom Duration: Jul 9 2017 → Jul 13 2017

Conference

Conference	29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017
Country/Territory	United Kingdom
City	London
Period	7/9/17 → 7/13/17

Keywords

Affine Schubert calculus
K-k-Schur function
K-rectangle factorization

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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title = "On some factorization formulas of K-k-Schur functions",

abstract = "We give some new formulas about factorizations of K-k-Schur functions gλ(k), analogous to the k-rectangle factorization formula sRt∪λ(k)= sRt(k)Sλ(k)of k-Schur functions, where λ is any k-bounded partition and Rt denotes the partition (tk+1-t) called a k-rectangle. Although a formula of the same form does not hold for K-k-Schur functions, we can prove that gRdivides gRt∪λ(k), and in fact more generally that gPdivides gP∪λ(k)for any multiple k-rectangles P and any k-bounded partition λ. We give the factorization formula of such gP(k), the explicit formulas of gP∪λ(k)/gP(k)in some cases.",

keywords = "Affine Schubert calculus, K-k-Schur function, K-rectangle factorization",

author = "Motoki Takigiku",

note = "Funding Information: The author would like to express his gratitude to T. Ikeda for suggesting the problem to the author and helping him with many fruitful discussions and advice. He is grateful to H. Hosaka and I. Terada for many valuable comments. This work was supported by the Program for Leading Graduate Schools, MEXT, Japan. The contents of this abstract, including their detailed proofs, are in the author{\textquoteright}s master-thesis. The full paper will be published elsewhere. Publisher Copyright: {\textcopyright} 29th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.; 29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017 ; Conference date: 09-07-2017 Through 13-07-2017",

year = "2006",

language = "English",

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T1 - On some factorization formulas of K-k-Schur functions

AU - Takigiku, Motoki

N1 - Funding Information: The author would like to express his gratitude to T. Ikeda for suggesting the problem to the author and helping him with many fruitful discussions and advice. He is grateful to H. Hosaka and I. Terada for many valuable comments. This work was supported by the Program for Leading Graduate Schools, MEXT, Japan. The contents of this abstract, including their detailed proofs, are in the author’s master-thesis. The full paper will be published elsewhere. Publisher Copyright: © 29th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.

PY - 2006

Y1 - 2006

N2 - We give some new formulas about factorizations of K-k-Schur functions gλ(k), analogous to the k-rectangle factorization formula sRt∪λ(k)= sRt(k)Sλ(k)of k-Schur functions, where λ is any k-bounded partition and Rt denotes the partition (tk+1-t) called a k-rectangle. Although a formula of the same form does not hold for K-k-Schur functions, we can prove that gRdivides gRt∪λ(k), and in fact more generally that gPdivides gP∪λ(k)for any multiple k-rectangles P and any k-bounded partition λ. We give the factorization formula of such gP(k), the explicit formulas of gP∪λ(k)/gP(k)in some cases.

AB - We give some new formulas about factorizations of K-k-Schur functions gλ(k), analogous to the k-rectangle factorization formula sRt∪λ(k)= sRt(k)Sλ(k)of k-Schur functions, where λ is any k-bounded partition and Rt denotes the partition (tk+1-t) called a k-rectangle. Although a formula of the same form does not hold for K-k-Schur functions, we can prove that gRdivides gRt∪λ(k), and in fact more generally that gPdivides gP∪λ(k)for any multiple k-rectangles P and any k-bounded partition λ. We give the factorization formula of such gP(k), the explicit formulas of gP∪λ(k)/gP(k)in some cases.

KW - Affine Schubert calculus

KW - K-k-Schur function

KW - K-rectangle factorization

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M3 - Paper

AN - SCOPUS:85091893872

T2 - 29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017

Y2 - 9 July 2017 through 13 July 2017

ER -

On some factorization formulas of K-k-Schur functions

Abstract

Conference

Keywords

ASJC Scopus subject areas

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