schur polynomial
Recently Published Documents


TOTAL DOCUMENTS

13
(FIVE YEARS 1)

H-INDEX

4
(FIVE YEARS 0)

10.37236/9354 ◽  
2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Per Alexandersson ◽  
Luis Angel González-Serrano ◽  
Egor Maximenko ◽  
Mario Alberto Moctezuma-Salazar

Given a symmetric polynomial $P$ in $2n$ variables, there exists a unique symmetric polynomial $Q$ in $n$ variables such that\[P(x_1,\ldots,x_n,x_1^{-1},\ldots,x_n^{-1})=Q(x_1+x_1^{-1},\ldots,x_n+x_n^{-1}).\] We denote this polynomial $Q$ by $\Phi_n(P)$ and show that $\Phi_n$ is an epimorphism of algebras. We compute $\Phi_n(P)$ for several families of symmetric polynomials $P$: symplectic and orthogonal Schur polynomials, elementary symmetric polynomials, complete homogeneous polynomials, and power sums. Some of these formulas were already found by Elouafi (2014) and Lachaud (2016). The polynomials of the form $\Phi_n(\operatorname{s}_{\lambda/\mu}^{(2n)})$, where $\operatorname{s}_{\lambda/\mu}^{(2n)}$ is a skew Schur polynomial in $2n$ variables, arise naturally in the study of the minors of symmetric banded Toeplitz matrices, when the generating symbol is a palindromic Laurent polynomial, and its roots can be written as $x_1,\ldots,x_n,x^{-1}_1,\ldots,x^{-1}_n$. Trench (1987) and Elouafi (2014) found efficient formulas for the determinants of symmetric banded Toeplitz matrices. We show that these formulas are equivalent to the result of Ciucu and Krattenthaler (2009) about the factorization of the characters of classical groups.



2020 ◽  
Vol 174 ◽  
pp. 105241 ◽  
Author(s):  
Arvind Ayyer ◽  
Ilse Fischer
Keyword(s):  


2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Huilan Li ◽  
Jennifer Morse ◽  
Pat Shields

International audience The problem of computing products of Schubert classes in the cohomology ring can be formulated as theproblem of expanding skew Schur polynomial into the basis of ordinary Schur polynomials. We reformulate theproblem of computing the structure constants of the Grothendieck ring of a Grassmannian variety with respect to itsbasis of Schubert structure sheaves in a similar way; we address the problem of expanding the generating functions forskew reverse-plane partitions into the basis of polynomials which are Hall-dual to stable Grothendieck polynomials. From this point of view, we produce a chain of bijections leading to Buch’s K-theoretic Littlewood-Richardson rule.



2019 ◽  
Vol 42 (18) ◽  
pp. 6459-6474
Author(s):  
Zhi‐Hua Zhang ◽  
Hari M. Srivastava
Keyword(s):  


Author(s):  
Sneha Sivaramakrishnan ◽  
Swathika Shunmugam ◽  
B. Bala Tripura Sundari


2008 ◽  
Vol 2008 (06) ◽  
pp. 101-101 ◽  
Author(s):  
Rajsekhar Bhattacharyya ◽  
Robert de Mello Koch ◽  
Michael Stephanou
Keyword(s):  


1997 ◽  
Vol 1 (1) ◽  
pp. 367-375 ◽  
Author(s):  
Axel Kohnert




1994 ◽  
Vol 205-206 ◽  
pp. 1271-1288
Author(s):  
Q.-H. Wu ◽  
M. Mansour


Sign in / Sign up

Export Citation Format

Share Document