2016
DOI: 10.48550/arxiv.1601.00047
|View full text |Cite
Preprint
|
Sign up to set email alerts
|

Bott-Samelson varieties and Poisson Ore extensions

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1

Citation Types

0
10
0

Year Published

2016
2016
2021
2021

Publication Types

Select...
7
1
1

Relationship

1
8

Authors

Journals

citations
Cited by 12 publications
(10 citation statements)
references
References 25 publications
0
10
0
Order By: Relevance
“…As far as we could tell, that would require that H have a rather fearsome Dynkin diagram, a sort of "broom" with handle of length n − 2 plus n + 1 bristles (nicely indexed by the covers of v(Y Spr ); see the final paragraph of the paper). It seems very hard to compute defining equations of strata inside such general Kac-Moody flag varieties; the closest work seems to be [EL19]. Much more recently we tried to embed the M-vdK poset (for small n) as an order ideal inside {ρ ∈ S m : ρ ≥ σ} for some fixed σ with X σ smooth (so that each X ρ…”
Section: Statement Of Resultsmentioning
confidence: 99%
“…As far as we could tell, that would require that H have a rather fearsome Dynkin diagram, a sort of "broom" with handle of length n − 2 plus n + 1 bristles (nicely indexed by the covers of v(Y Spr ); see the final paragraph of the paper). It seems very hard to compute defining equations of strata inside such general Kac-Moody flag varieties; the closest work seems to be [EL19]. Much more recently we tried to embed the M-vdK poset (for small n) as an order ideal inside {ρ ∈ S m : ρ ≥ σ} for some fixed σ with X σ smooth (so that each X ρ…”
Section: Statement Of Resultsmentioning
confidence: 99%
“…In §4, we discuss the theory of global R-matrices developed by Weinstein and Xu in [19]. We show that for the Drinfeld double (D, π D ) of a pair ((G, π G ), (G * , π G * )) of dual Poisson Lie groups, the global R-matrix is, under an appropriate isomorphism, the cartesian product in Γ 4 of L and the identity bisections in Γ G and Γ G * , where L is as in (1). Section §5 is where the first main result of this paper, Theorem 5.4, appears.…”
Section: Introductionmentioning
confidence: 91%
“…Throughout this paper, by a local Lie groupoid, we will mean a 3-associative local Lie groupoid in the sense of [2,Definition 2.7]. That is, a manifold G equipped with submersions θ, τ : G → Y to a base manifold Y , an embedding ε : Y → G, a multiplication defined on an open neighbourhood G 1) of an open neighbourhood G (−1) ⊂ G of ε(Y ), and satisfying the usual axioms of a Lie groupoid wherever these make sense. A local Poisson groupoid is a pair (G ⇒ Y, π) where G ⇒ Y is a local Lie groupoid, and π a Poisson bivector field on G such that the graph of the multiplication Let (G ⇒ Y, π) be a symplectic groupoid over (Y, π Y ) with source map θ : G → Y , let (X, π X ) be a Poisson manifold with a map µ : X → Y , and let…”
Section: Poisson Actions Of Double Symplectic Groupoidsmentioning
confidence: 99%
“…Varieties that appear in the theory of Poisson Lie groups and Poisson homogeneous spaces provide numerous examples of Poisson-CGL extensions, see for example [13] for coordinate rings of Schubert cells and affine charts of Bott-Samelson varieties. The coordinate rings of such varieties are semiclassical limits of quantized algebras of functions and the above axioms are Poisson incarnations of the Levendorskii-Soibelman straightening law for quantum groups [5,Proposition I.6.10].…”
mentioning
confidence: 99%