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Clifford algebra analogue of Cartan's theorem for symmetric pairs

Research output: Working paper › Preprint

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Clifford algebra analogue of Cartan's theorem for symmetric pairs. / Calvert, Kieran; Grizelj, Karmen; Krutov, Andrey et al.
2025.

Research output: Working paper › Preprint

Harvard

Calvert, K, Grizelj, K, Krutov, A & Pandžić, P 2025 'Clifford algebra analogue of Cartan's theorem for symmetric pairs'.

APA

Calvert, K., Grizelj, K., Krutov, A., & Pandžić, P. (2025). Clifford algebra analogue of Cartan's theorem for symmetric pairs.

Vancouver

Calvert K, Grizelj K, Krutov A, Pandžić P. Clifford algebra analogue of Cartan's theorem for symmetric pairs. 2025 Apr 29.

Author

Calvert, Kieran ; Grizelj, Karmen ; Krutov, Andrey et al. / Clifford algebra analogue of Cartan's theorem for symmetric pairs. 2025.

Bibtex

@techreport{8fbd3896089849e18950a88b3addee95,
title = "Clifford algebra analogue of Cartan's theorem for symmetric pairs",
abstract = " We extend Kostant's results about $\mathfrak{g}$-invariants in the Clifford algebra $Cl(\mathfrak{g})$ of a complex semisimple Lie algebra $\mathfrak{g}$ to the relative case of $\mathfrak{k}$-invariants in the Clifford algebra $Cl(\mathfrak{p})$, where $(\mathfrak{g},\mathfrak{k})$ is a classical symmetric pair and $\mathfrak{p}$ is the $(-1)$-eigenspace of the corresponding involution. In this setup we prove the Cartan theorem for Clifford algebras, a relative transgression theorem, the Harish--Chandra isomorphism for $Cl(\mathfrak{p})$, and a relative version of Kostant's Clifford algebra conjecture. ",
keywords = "math.RT, math.DG, 17B20, 22E60, 57T15, 57R91",
author = "Kieran Calvert and Karmen Grizelj and Andrey Krutov and Pavle Pand{\v z}i{\'c}",
note = "47 pages",
year = "2025",
month = apr,
day = "29",
language = "English",
type = "WorkingPaper",

}

RIS

TY - UNPB

T1 - Clifford algebra analogue of Cartan's theorem for symmetric pairs

AU - Calvert, Kieran

AU - Grizelj, Karmen

AU - Krutov, Andrey

AU - Pandžić, Pavle

N1 - 47 pages

PY - 2025/4/29

Y1 - 2025/4/29

N2 - We extend Kostant's results about $\mathfrak{g}$-invariants in the Clifford algebra $Cl(\mathfrak{g})$ of a complex semisimple Lie algebra $\mathfrak{g}$ to the relative case of $\mathfrak{k}$-invariants in the Clifford algebra $Cl(\mathfrak{p})$, where $(\mathfrak{g},\mathfrak{k})$ is a classical symmetric pair and $\mathfrak{p}$ is the $(-1)$-eigenspace of the corresponding involution. In this setup we prove the Cartan theorem for Clifford algebras, a relative transgression theorem, the Harish--Chandra isomorphism for $Cl(\mathfrak{p})$, and a relative version of Kostant's Clifford algebra conjecture.

AB - We extend Kostant's results about $\mathfrak{g}$-invariants in the Clifford algebra $Cl(\mathfrak{g})$ of a complex semisimple Lie algebra $\mathfrak{g}$ to the relative case of $\mathfrak{k}$-invariants in the Clifford algebra $Cl(\mathfrak{p})$, where $(\mathfrak{g},\mathfrak{k})$ is a classical symmetric pair and $\mathfrak{p}$ is the $(-1)$-eigenspace of the corresponding involution. In this setup we prove the Cartan theorem for Clifford algebras, a relative transgression theorem, the Harish--Chandra isomorphism for $Cl(\mathfrak{p})$, and a relative version of Kostant's Clifford algebra conjecture.

KW - math.RT

KW - math.DG

KW - 17B20, 22E60, 57T15, 57R91

M3 - Preprint

BT - Clifford algebra analogue of Cartan's theorem for symmetric pairs

ER -