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## PBW filtration and bases for symplectic Lie algebras

International Mathematics Research Notices. 2011. Vol. 2011. No. 24. P. 5760-5784.

We study the PBW filtration on the highest weight representations V(λ) of sp2n. This
filtration is induced by the standard degree filtration on U(n−). We give a description
of the associated graded S(n−)-module gr V(λ) in terms of generators and relations. We
also construct a basis of gr V(λ). As an application we derive a graded combinatorial
formula for the character of V(λ) and obtain a new class of bases of the modules V(λ).

Research target:
Philosophy, Ethics, and Religious Studies

Language:
English

Turkensteen M., Ghosh D., Goldengorin B. I. et al., European Journal of Operational Research 2008 Vol. 189 No. 3 P. 775-788

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Marshakov A., Mironov A., Morozov A., Journal of High Energy Physics 2009 No. 11(048) P. 1-15

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family of commutative subalgebras, called the quantum shift of argument
subalgebras math.RT/0606380 , math.QA/0612798 . We prove that generically their
action on finite-dimensional modules is diagonalizable and their joint spectra
are in bijection with the set of monodromy-free opers for the Langlands dual ...

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The Cayley-Hamilton-Newton identities which generalize both the characteristic identity and the Newton relations have been recently obtained for the algebras of the RTT-type. We extend this result to a wider class of algebras M(ˆR, ˆ F) defined by a pair of compatible
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This paper is the first in a series that describe a conjectural analog of the geometric Satake isomorphism for an affine Kac-Moody group (in this paper for simplicity we consider only untwisted and simply connected case). The usual geometric Satake isomorphism for a reductive group G identifies the tensor category Rep(G_) of finitedimensional representations of ...

Added: October 12, 2012

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Modifications of bundles over complex curves is an operation that allows one to
construct a new bundle from a given one. Modifications can change a topological type of
bundle. We describe the topological type in terms of the characteristic classes of the bundle.Being applied to the Higgs bundles modifications establish an equivalence between different classical integrable systems. ...

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Moraru R., Verbitsky M., Central European Journal of Mathematics 2010 Vol. 8 No. 2 P. 327-337

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The main goal of the article is to give the definition of algebraic stability that
would permit us to consider stability, not only for algebraic vector bundles or
torsion-free coherent sheaves, but for the abelian category of coherent sheaves or
for whatever abelian category. We present an axiomatic description of the algebraic
stability on an abelian category and prove ...

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Kolesnikov A., Banakh T., Bogachev V., Functional Analysis and Its Applications 2004 P. 23-47

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Marshakov A., Theoretical and Mathematical Physics 2011 Vol. 169 No. 3 P. 1704-1723

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Liviu O., Verbitsky M., International Mathematics Research Notices 2012 No. 4 P. 894-903

A manifold M is locally conformally Kähler (LCK), if it admits a Kähler covering with monodromy acting by holomorphic homotheties. For a compact connected group G acting on an LCK manifold by holomorphic automorphisms, an averaging procedure gives a G-invariant LCK metric. Suppose that S1 acts on an LCK manifold M by holomorphic isometries, and ...

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Amerik E., Proceedings of the Edinburgh Mathematical Society 2011 Vol. 51 No. 1 P. 1-7

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Series C., Bufetov A. I., Mathematical Proceedings of the Cambridge Philosophical Society 2011 Vol. 151 No. 1 P. 145-159

We use Series' Markovian coding for words in Fuchsian groups and the
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Alcaraz F. C., Pyatov P. N., Rittenberg V., Journal of Statistical Mechanics: Theory and Experiment 2008 Vol. P01006 P. 1-38

We consider the raise and peel model of a one-dimensional fluctuating interface in
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the stationary states, several density profiles are studied usingMonte Carlo simulations. We point out a ...

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Goldengorin B. I., Jager G., Algorithmic Operational Research 2008 Vol. 3 No. 1 P. 79-81

Added: July 31, 2012