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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