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  • 2411.11663v1

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Clifford algebras and Littlewood-Richardson coefficients

Research output: Working paper › Preprint

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Clifford algebras and Littlewood-Richardson coefficients. / Calvert, Kieran; Grizelj, Karmen; Krutov, Andrey et al.
Arxiv, 2024.

Research output: Working paper › Preprint

Harvard

Calvert, K, Grizelj, K, Krutov, A & Pandžić, P 2024 'Clifford algebras and Littlewood-Richardson coefficients' Arxiv.

APA

Calvert, K., Grizelj, K., Krutov, A., & Pandžić, P. (2024). Clifford algebras and Littlewood-Richardson coefficients. Arxiv.

Vancouver

Calvert K, Grizelj K, Krutov A, Pandžić P. Clifford algebras and Littlewood-Richardson coefficients. Arxiv. 2024 Nov 18.

Author

Calvert, Kieran ; Grizelj, Karmen ; Krutov, Andrey et al. / Clifford algebras and Littlewood-Richardson coefficients. Arxiv, 2024.

Bibtex

@techreport{448bfd8bf33e46069d8bec93cb5f60a7,
title = "Clifford algebras and Littlewood-Richardson coefficients",
abstract = "We show how to use Clifford algebra techniques to describe the de Rham cohomology ring of equal rank compact symmetric spaces $G/K$. In particular, for $G/K=U(n)/U(k)\times U(n-k)$, we obtain a new way of multiplying Schur polynomials, i.e., computing the Littlewood-Richardson coefficients. The corresponding multiplication on the Clifford algebra side is, in a convenient basis given by projections of the spin module, simply the componentwise multiplication of vectors in $\mathbb{C}^N$, also known as the Hadamard product. ",
keywords = "math.RT, 22E47, 14N15, 05E05",
author = "Kieran Calvert and Karmen Grizelj and Andrey Krutov and Pavle Pand{\v z}i{\'c}",
note = "10 pages",
year = "2024",
month = nov,
day = "18",
language = "English",
publisher = "Arxiv",
type = "WorkingPaper",
institution = "Arxiv",

}

RIS

TY - UNPB

T1 - Clifford algebras and Littlewood-Richardson coefficients

AU - Calvert, Kieran

AU - Grizelj, Karmen

AU - Krutov, Andrey

AU - Pandžić, Pavle

N1 - 10 pages

PY - 2024/11/18

Y1 - 2024/11/18

N2 - We show how to use Clifford algebra techniques to describe the de Rham cohomology ring of equal rank compact symmetric spaces $G/K$. In particular, for $G/K=U(n)/U(k)\times U(n-k)$, we obtain a new way of multiplying Schur polynomials, i.e., computing the Littlewood-Richardson coefficients. The corresponding multiplication on the Clifford algebra side is, in a convenient basis given by projections of the spin module, simply the componentwise multiplication of vectors in $\mathbb{C}^N$, also known as the Hadamard product.

AB - We show how to use Clifford algebra techniques to describe the de Rham cohomology ring of equal rank compact symmetric spaces $G/K$. In particular, for $G/K=U(n)/U(k)\times U(n-k)$, we obtain a new way of multiplying Schur polynomials, i.e., computing the Littlewood-Richardson coefficients. The corresponding multiplication on the Clifford algebra side is, in a convenient basis given by projections of the spin module, simply the componentwise multiplication of vectors in $\mathbb{C}^N$, also known as the Hadamard product.

KW - math.RT

KW - 22E47, 14N15, 05E05

M3 - Preprint

BT - Clifford algebras and Littlewood-Richardson coefficients

PB - Arxiv

ER -