The regular semisimple locus of the affine quotient of the cotangent bundle of the Grothendieck-Springer resolution

JOURNAL OF GEOMETRY AND PHYSICS

卷:132

Article

Im, Mee Seong^1,2 

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[2] US Mil Acad, Dept Math Sci, West Point, NY 10996 USA

关键词: Hamiltonian reduction of an enhanced Borel subalgebra;    Grothendieck-Springer resolutions;    Moment maps;    Regular semisimple locus;    Generalized almost-commuting varieties;    Hilbert schemes for nonreductive groups;   

DOI  :  10.1016/j.geomphys.2018.05.022

来源: Elsevier

【 摘 要 】

Let G = GL(n)(C), the general linear group over the complex numbers, and let B be the set of invertible upper triangular matrices in G. Let b = Lie(B). For mu : T*(b x C-n) -> b*, where b* congruent to g/u and u being strictly upper triangular matrices in g = Lie(G), we prove that the Hamiltonian reduction mu(-1)(0)(rss)//B of the extended regular semisimple locus b(rss) of the Borel subalgebra is smooth, affine, reduced, and scheme-theoretically isomorphic to a dense open locus of C-2n. We also show that the B-invariant functions on the regular semisimple locus of the Hamiltonian reduction of b x C-n arise as the trace of a certain product of matrices. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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