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Feigin, Evgeny ORCID: 0000-0001-7390-1879, Finkelberg, Michael ORCID: 0000-0002-1977-2305 and Littelmann, Peter (2014). Symplectic Degenerate Flag Varieties. Can. J. Math.-J. Can. Math., 66 (6). S. 1250 - 1287. CAMBRIDGE: CAMBRIDGE UNIV PRESS. ISSN 1496-4279

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Abstract

A simple finite dimensional module V-lambda of a simple complex algebraic group G is naturally endowed with a filtration induced by the PBW-filtration of U(Lie G). The associated graded space 11, is a module for the group G(a), which can be roughly described as a semi-direct product of a Borel subgroup of G and a large commutative unipotent group G(a)(M). In analogy to the flag variety F-lambda= G.[v(lambda)] subset of P(V-lambda), we call the closure (G(a).[v(lambda)]) over bar subset of P(V-lambda(a)) of the G(a)-orbit through the highest weight line the degenerate flag variety F-lambda(a). In general this is a singular variety, but we conjecture that it has many nice properties similar to that of Schubert varieties. In this paper we consider the case of G being the symplectic group. The symplectic case is important for the conjecture because it is the first known case where, even for fundamental weights w, the varieties F-w(a) differ from F-w. We give an explicit construction of the varieties Sp F-lambda(a) and construct desingularizations, similar to the Bott-Samelson resolutions in the classical case. We prove that Sp F-lambda(a) are normal locally complete intersections with terminal and rational singularities. We also show that these varieties are Frobenius split. Using the above mentioned results, we prove an analogue of the Borel Weil theorem and obtain a q-character formula for the characters of irreducible Sp(2n)-modules via the Atiyah-Bott-Lefschetz fixed points formula.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Feigin, Evgeny UNSPECIFIED orcid.org/0000-0001-7390-1879 UNSPECIFIED Finkelberg, Michael UNSPECIFIED orcid.org/0000-0002-1977-2305 UNSPECIFIED Littelmann, Peter UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-422097
DOI:	10.4153/CJM-2013-038-6
Journal or Publication Title:	Can. J. Math.-J. Can. Math.
Volume:	66
Number:	6
Page Range:	S. 1250 - 1287
Date:	2014
Publisher:	CAMBRIDGE UNIV PRESS
Place of Publication:	CAMBRIDGE
ISSN:	1496-4279
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language FORMULA Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/42209