Bruhat order in the Toda system on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e37" altimg="si2.gif"><mml:mi mathvariant="fraktur">so</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>4</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>: An example of non-split real form

Chernyakov, Yu. B.; Sharygin, G.; Сорин, А.С.

doi:10.1016/j.geomphys.2018.10.015

Cited by 6 publications

(3 citation statements)

References 13 publications

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“…Also observe that in our other papers [6,11] we used explicit computations to show that similar statements hold for all real groups of rank 2 and for the non-split real form, SO (2,4). In the latter case the role of Weyl group is played by the group W (g, k) = N K (a)/Z K (a) where N K , Z K are the (non-discrete) normalizer and centralizer of a in K. One can show that W (g, k) is again a Coxeter group, thus we can introduce Bruhat order on it.…”

Section: Resultssupporting

confidence: 62%

The Full Symmetric Toda Flow and Intersections of Bruhat Cells

Chernyakov

Sharygin

Сорин

et al. 2020

SIGMA

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Section: Resultssupporting

confidence: 62%

The Full Symmetric Toda Flow and Intersections of Bruhat Cells

Chernyakov

Sharygin

Сорин

et al. 2020

SIGMA

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“…Also observe that in our following papers ( [4,5]) we used explicit computations to show that similar statements hold for all real groups of rank 2 and for the non-split real form, SO(2, 4). In the latter case the role of Weyl group is played by the group W (g, k) = N K (a)/Z K (a), where N K , Z K are the (non-discrete) normalizer and centralizer of a in K; one can show, that W (g, k) is again Coxeter group, thus we can introduce Bruhat order on it.…”

Section: Introduction and The Statement Of Resultsmentioning

confidence: 76%

The Full Symmetric Toda Flow and Intersections of Bruhat Cells

Chernyakov,

Sharygin,

Sorin

et al. 2018

Preprint

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In this short note we show that the Bruhat cells in real normal forms of semisimple Lie algebras enjoy the same property as their complex analogs: for any two elements w, w ′ in the Weyl group W (g), the corresponding real Bruhat cell X w intersects with the dual Bruhat cell Y w ′ iff w ≺ w ′ in the weak Bruhat order on W (g). Here g is a normal real form of a semisimple complex Lie algebra g C . Our reasoning is based on the properties of the Toda flows, rather than on the analysis of the Weyl group action and geometric considerations.

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confidence: 99%

On the invariants of the full symmetric Toda system

Chernyakov¹,

Sharygin²,

Сорин³

2019

Preprint

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In this paper we continue our study of the geometric properties of full symmetric Toda systems from [1,2,3]. Namely we describe here a simple geometric construction of a commutative family of vector fields on compact groups, that include the Toda vector field, i.e. the field, which generates the full symmetric Toda system associated with the Cartan decomposition of a semisimple Lie algebra. Our construction makes use of the representations of the semisimple algebra and does not depend on the splitness of the Cartan pair. It is very close to the family of invariants and semiinvariants of the Toda system associted with SL n , introduced in [4].

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Bruhat order in the Toda system on so(2,4): An example of non-split real form

Cited by 6 publications

References 13 publications

The Full Symmetric Toda Flow and Intersections of Bruhat Cells

The Full Symmetric Toda Flow and Intersections of Bruhat Cells

The Full Symmetric Toda Flow and Intersections of Bruhat Cells

On the invariants of the full symmetric Toda system

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