scholarly journals PLÜCKER RELATIONS AND SPHERICAL VARIETIES: APPLICATION TO MODEL VARIETIES

2014 ◽  
Vol 19 (4) ◽  
pp. 979-997 ◽  
Author(s):  
ROCCO CHIRIVÌ ◽  
ANDREA MAFFEI
Keyword(s):  
Spherical Varieties ◽  
Plücker Relations

scholarly journals Complete intersections in spherical varieties

2016 ◽  
Vol 22 (4) ◽  
pp. 2099-2141 ◽  
Author(s):  
Kiumars Kaveh ◽  
A. G. Khovanskii
Keyword(s):  
Complete Intersections ◽  
Spherical Varieties

scholarly journals Semi-infinite Plücker Relations and Weyl Modules

2018 ◽  
Vol 2020 (14) ◽  
pp. 4357-4394 ◽  
Author(s):  
Evgeny Feigin ◽  
Ievgen Makedonskyi
Keyword(s):  
Type A ◽  
Character Formula ◽  
Flag Varieties ◽  
Coordinate Ring ◽  
Weyl Modules ◽  
Plücker Relations ◽  
Plücker Embedding ◽  
Formal Version ◽  
The Ideal

Abstract The goal of this paper is two-fold. First, we write down the semi-infinite Plücker relations, describing the Drinfeld–Plücker embedding of the (formal version of) semi-infinite flag varieties in type A. Second, we study the homogeneous coordinate ring, that is, the quotient by the ideal generated by the semi-infinite Plücker relations. We establish the isomorphism with the algebra of dual global Weyl modules and derive a new character formula.

scholarly journals Periodic Staircase Matrices and Generalized Cluster Structures

2020 ◽  
Author(s):  
Misha Gekhtman ◽  
Michael Shapiro ◽  
Alek Vainshtein
Keyword(s):  
Difference Operators ◽  
Drinfeld Double ◽  
Similar Role ◽  
Geometric Type ◽  
Plücker Relations ◽  
Lie Brackets

Abstract As is well known, cluster transformations in cluster structures of geometric type are often modeled on determinant identities, such as short Plücker relations, Desnanot–Jacobi identities, and their generalizations. We present a construction that plays a similar role in a description of generalized cluster transformations and discuss its applications to generalized cluster structures in $GL_n$ compatible with a certain subclass of Belavin–Drinfeld Poisson–Lie brackets, in the Drinfeld double of $GL_n$, and in spaces of periodic difference operators.

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