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Titlebook: Representations and Nilpotent Orbits of Lie Algebraic Systems; In Honour of the 75t Maria Gorelik,Vladimir Hinich,Anna Melnikov Book 2019 S

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On Cacti and Crystals,stal bases for any symmetrizable Kac–Moody algebra .. The most notable of them are the cactus group and (yet conjectural) Weyl group action on any highest weight integrable module and its lower and upper crystal bases. Surprisingly, some generators of cactus groups are anti-involutions of the Gelfan
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On Involutions in the Weyl Group and ,-Orbit Closures in the Orthogonal Case, To each basis involution . in the Weyl group . of . one can assign the associated .-orbit Ω.. We prove that, given basis involutions ., . in ., if the orbit Ω. is contained in the closure of the orbit Ω. then . is less than or equal to . with respect to the Bruhat order on .. For a basis involution
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The Spin Calogero-Sutherland Model at Infinity,s action is given by the Heckman operators (1991) via the Drinfeld functor (1986). We describe the limit of this action at . →. . This provides another solution to the problem already considered by Khoroshkin, Matushko and Sklyanin (2017).
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