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Mathematics > Differential Geometry

arXiv:2201.03109 (math)
[Submitted on 9 Jan 2022 (v1), last revised 19 Feb 2022 (this version, v2)]

Title:Local Plücker formulas for orthogonal groups

Authors:Denis Degtyarev
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Abstract:Local Plücker formulas relate the vector of metrics on a holomorphic curve in the projective space, induced by the Fubini-Study metrics on projetive spaces via Plücker embeddings of associated curves, to the corresponding vector of curvatures. Givental noted that the vector of curvatures is expressed in terms of the vector of metrics via Cartan matrix of type $ A_n$ and extended this observation from type $A_n$ to all nonexceptional types. In this paper we show how local Plücker formulas for special orthogonal groups, i.e. for Cartan matrices of type $ B_n$ and $ D_n$, can be obtained by reduction to the classical $A_n$ case.
Subjects: Differential Geometry (math.DG); Algebraic Geometry (math.AG); Representation Theory (math.RT)
Cite as: arXiv:2201.03109 [math.DG]
  (or arXiv:2201.03109v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.2201.03109

Submission history

From: Denis Degtyarev [view email]
[v1] Sun, 9 Jan 2022 23:34:35 UTC (9 KB)
[v2] Sat, 19 Feb 2022 10:03:50 UTC (9 KB)
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