Coadjoint orbits of the group UT(7, K)

Ignatev, M. V.; Panov, A. N.

doi:10.1007/s10958-008-9267-0

Cited by 8 publications

(13 citation statements)

References 5 publications

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“…It turns out that almost all coadjoint orbit studied to the moment are associated with certain D and ξ, see, e.g., [An95], [AN06], [Ko12], [Ko13], [Pa08], [IPa09], [Ig09], [Ig11], [Ig12]. On the other hand, C.A.M.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Rook placements in $G_2$ and $F_4$ and associated coadjoint orbits

Ignatev¹,

A.²

2021

Preprint

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Let n be a maximal nilpotent subalgebra of a simple complex Lie algebra with root system Φ. A subset D of the set Φ + of positive roots is called a rook placement if it consists of roots with pairwise non-positive scalar products. To each rook placement D and each map ξ from D to the set C × of nonzero complex numbers one can naturally assign the coadjoint orbit Ω D,ξ in the dual space n * . By definition, Ω D,ξ is the orbit of f D,ξ , where f D,ξ is the sum of root covectors e * α multiplied by ξ(α), α ∈ D. (In fact, almost all coadjoint orbits studied at the moment have such a form for certain D and ξ.) It follows from the results of Andrè that if ξ 1 and ξ 2 are distinct maps from D to C × then Ω D,ξ1 and Ω D,ξ2 do not coincide for classical root systems Φ. We prove that this is true if Φ is of type G 2 , or if Φ is of type F 4 and D is orthogonal.

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Section: Introduction and The Main Resultsmentioning

confidence: 99%

Rook placements in $G_2$ and $F_4$ and associated coadjoint orbits

Ignatev¹,

A.²

2021

Preprint

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“…A character of irreducible representation, associated with a subregular coadjoint orbit, is called a subregular character. Subregular coadjoint orbits of the group UT(n, R) were classified in [4]. Basing on this classification we obtain formulas (theorems 3.3 and 3.6) for subregular characters.…”

Section: Introductionmentioning

confidence: 99%

Subregular Characters of the Group UT(n, ℝ)

Panov

Suray

2014

J Math Sci

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“…The squares (t, a) and (i, k)) are filled by symbol ⊗. In Example 1, the square (7,4) is filled by symbol • and has type 1, a = 1 and k = 2. The squares (4, 1) and (7,2) are filled by symbol ⊗.…”

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confidence: 99%

“…The associated coadjoint orbit of this involution is a subregular orbit (i.e. orbit of dimension dim(reg.orbit) − 2) (see [4]). The defining ideal I(Ω(f )) is generated by…”

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confidence: 99%