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19 pages, 536 KiB

Open AccessFeature PaperArticle

Heisenberg Parabolic Subgroup of SO^∗(10) and Invariant Differential Operators

by V. K. Dobrev

Symmetry 2022, 14(8), 1592; https://doi.org/10.3390/sym14081592 - 3 Aug 2022

Cited by 1 | Viewed by 1479

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra

s o^{*} (10)

. We use the maximal Heisenberg parabolic subalgebra

P = M \oplus A \oplus N

[...] Read more.

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra

s o^{*} (10)

. We use the maximal Heisenberg parabolic subalgebra

P = M \oplus A \oplus N

with

M = s u (3, 1) \oplus s u (2) ≅ s o^{*} (6) \oplus s o (3)

. We give the main and the reduced multiplets of indecomposable elementary representations. This includes the explicit parametrization of the intertwining differential operators between the ERS. Due to the recently established parabolic relations the multiplet classification results are valid also for the algebras

s o (p, q)

(with

p + q = 10

p \geq q \geq 2

) with maximal Heisenberg parabolic subalgebra:

P^{'} = M^{'} \oplus A^{'} \oplus N^{'}

M^{'} = s o (p - 2, q - 2) \oplus s l (2, I R)

M^{' C} ≅ M^{C}

. Full article

(This article belongs to the Section Physics)

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12 pages, 434 KiB

Open AccessArticle

Heisenberg Parabolic Subgroups of Exceptional Non-Compact G₂₍₂₎ and Invariant Differential Operators

by V.K. Dobrev

Symmetry 2022, 14(4), 660; https://doi.org/10.3390/sym14040660 - 24 Mar 2022

Cited by 1 | Viewed by 2060

Abstract

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra

G_{2 (2)}

. We use both the minimal and the maximal Heisenberg parabolic subalgebras. We give the main [...] Read more.

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra

G_{2 (2)}

. We use both the minimal and the maximal Heisenberg parabolic subalgebras. We give the main multiplets of indecomposable elementary representations. This includes the explicit parametrization of the intertwining differential operators between the ERs. These are new results applicable in all cases when one would like to use

G_{2 (2)}

invariant differential operators. Full article

(This article belongs to the Special Issue Manifest and Hidden Symmetries in Field and String Theories)

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