Small Resolutions of Schubert Varieties in Symplectic and Orthogonal Grassmannians | Zendy

Parameswaran Sankaran | Zendy; P. Vanchinathan | Zendy

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Small Resolutions of Schubert Varieties in Symplectic and Orthogonal Grassmannians

Author(s) -

Parameswaran Sankaran,

P. Vanchinathan

Publication year - 1994

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195165906

Subject(s) - mathematics , algebraic group , borel subgroup , maximal torus , weyl group , combinatorics , symplectic geometry , orbit (dynamics) , schubert variety , symplectic group , fixed point , reductive group , group (periodic table) , torus , pure mathematics , algebraic number , geometry , mathematical analysis , lie algebra , group theory , physics , fundamental representation , quantum mechanics , engineering , weight , aerospace engineering

Let G be a semisimple algebraic group over C, and B a Borel subgroup of G. Let P be a parabolic subgroup of G that contains B. Denote by W the Weyl group of G with respect to a fixed maximal torus T c B, and let WP a W be the Weyl group of P. We denote the set of minimal representatives of W/Wp by W. For coeW, X(co) denotes the Schubert variety in G/P corresponding to co. X(co) is the Zariski closure of the B-orbit of a unique T-fixed point ew of G/P. We call ew 'the centre' of X(a)). Our conventions for labelling the simple roots in W are the same as in [1].

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