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Algebra and Lie Theory Seminar

Mondays at 14:15
Research I, Room 111

The Algebra and Lie Theory Seminar is a graduate research seminar.

This semester we will concentrate on the structure of diagonal Lie algebras and on the Fernando-Kac subalgebras of generalized Harish Chandra modules.

Special Event: Minicourse on Geometry of Grassmannians

Evgeny Smirnov (Universität Bonn), Research I Seminar Room

Monday, March 9, 13:45 Grassmannians. Schubert varieties. Cohomology ring of a Grassmannian. Poincaré duality. Pieri formula. Littlewood-Richardson rule (w/o proof). Applications to enumerative problems.
Tuesday, March 10, 15:15 Singularities of Schubert varieties: Bott-Samelson resolutions. Zelevinsky's small resolutions.
Wednesday, March 11, 17:00 Plücker embedding. Plücker relations. Standard monomials. Plücker relations generate the homogeneous ideal of a Grassmannian. Desription of the singular loci of Schubert varieties.

Special Event: Minicourse on Geometry of Flag Varieties

Valentina Kiritchenko (Jacobs University), Research I Seminar Room

Monday, April 27, 13:45 Varieties of complete flags. Main example: complete flags in a 3-space. Picard group of a flag variety and irreducible representations of semisimple groups. Borel presentation for the cohomology ring of a flag variety.
Monday, May 4, 13:45 Bruhat cell decomposition, Bruhat order, Schubert cycles. Schubert cycles in the Borel presentation, divided difference operators, Schubert polynomials.
Monday, May 11, 13:45 Schubert calculus, Chevalley-Pieri formula for the product of a Schubert cycle with a divisor. Bott-Samelson resolutions of Schubert cycles in a flag variety.


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