I. M. Pevzner, “Orbits of vectors in some representations”, Problems in the theory of representations of algebras and groups. Part 35, Zap. Nauchn. Sem. POMI, 484, POMI, St. Petersburg, 2019, 149

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Zapiski Nauchnykh Seminarov POMI, 2019, Volume 484, Pages 149–164 (Mi znsl6864)

This article is cited in 2 scientific papers (total in 2 papers)

Orbits of vectors in some representations

I. M. Pevzner

Herzen State Pedagogical University of Russia, St. Petersburg

Full-text PDF (225 kB) Citations (2)

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Abstract: Let

Φ

$\Phi$ be a root system of type

E_{6}

$E_6$ ,

E_{7}

$E_7$ , or

E_{8}

$E_8$ . Let

K

$K$ be a field of characteristic not

2

$2$ . Let

δ

$\delta$ be the maximal root of

Φ

$\Phi$ and set

Φ_{0} = {α \in Φ; δ ⊥ α}

$\Phi_0 = \{\alpha\in\Phi; \delta\perp\alpha\}$ . We describe orbits of the group

G_{s c} (Φ_{0}, K)

$G_{\mathrm{sc}}(\Phi_0, K)$ acting on the set

⟨ e_{α}; ∠ (α, δ) = π / 3 ⟩

$\langle e_\alpha; \angle(\alpha, \delta) = \pi/3\rangle$ .

Key words and phrases: Сhevalley groups, orbits of vectors, root elements.

Funding agency	Grant number
Russian Foundation for Basic Research	19-01-00297

Received: 09.09.2019

Document Type: Article

UDC: 512.5

Language: Russian

Citation: I. M. Pevzner, “Orbits of vectors in some representations”, Problems in the theory of representations of algebras and groups. Part 35, Zap. Nauchn. Sem. POMI, 484, POMI, St. Petersburg, 2019, 149–164

Citation in format AMSBIB

\Bibitem{Pev19}

\by I.~M.~Pevzner

\paper Orbits of vectors in some representations

\inbook Problems in the theory of representations of algebras and groups. Part~35

\serial Zap. Nauchn. Sem. POMI

\yr 2019

\vol 484

\pages 149--164

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl6864}

Linking options:

https://www.mathnet.ru/eng/znsl6864

https://www.mathnet.ru/eng/znsl/v484/p149

Cycle of papers

Orbits of vectors in some representations
I. M. Pevzner
Zap. Nauchn. Sem. POMI, 2019, 484, 149–164
Orbits of vectors in some representations. II
I. M. Pevzner
Zap. Nauchn. Sem. POMI, 2023, 522, 125–151
Orbits of vectors in some representations. III
I. M. Pevzner
Zap. Nauchn. Sem. POMI, 2023, 522, 152–163

This publication is cited in the following 2 articles:

I. M. Pevzner, “Orbity vektorov nekotorykh predstavlenii. II”, Voprosy teorii predstavlenii algebr i grupp. 39, Zap. nauchn. sem. POMI, 522, POMI, SPb., 2023, 125–151
I. M. Pevzner, “Orbity vektorov nekotorykh predstavlenii. III”, Voprosy teorii predstavlenii algebr i grupp. 39, Zap. nauchn. sem. POMI, 522, POMI, SPb., 2023, 152–163

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	178
Full-text PDF :	48
References:	39

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