The Last Possible Place of Unitarity for Certain Highest Weight Modules.
The Leibniz algebras whose subalgebras are ideals
In this paper we obtain the description of the Leibniz algebras whose subalgebras are ideals.
The Lie algebra cohomology of jets.
The Lie algebra of endomorphisms of an infinite-dimensional vector space
The Magic Square and symmetric Compositions.
The new construction given by Barton and Sudbery of the Freudenthal-Tits magic square, which includes the exceptional classical simple Lie algebras, will be interpreted and extended by using a pair of symmetric composition algebras, instead of the standard unital composition algebras.
The Magic Square and Symmetric Compositions II.
The mathematics of fivebranes.
The meaning of time and covariant superderivatives in supermechanics.
The Minimal Condition for Subideals of Lie Algebras.
The minimal orbit in a simple Lie algebra and its associated maximal ideal
The multisegment duality and the preprojective algebras of type .
The triplet vertex operator superalgebras: twisted sector.
The -cohomology of representations with an infinitesimal character
The -Lie property of the Jacobian as a condition for complete integrability.
The Nekrasov-Okounkov hook length formula: refinement, elementary proof, extension and applications
The paper is devoted to the derivation of the expansion formula for the powers of the Euler Product in terms of partition hook lengths, discovered by Nekrasov and Okounkov in their study of the Seiberg-Witten Theory. We provide a refinement based on a new property of -cores, and give an elementary proof by using the Macdonald identities. We also obtain an extension by adding two more parameters, which appears to be a discrete interpolation between the Macdonald identities and the generating function...
The nil Hecke ring and Deodhar's conjecture on Bruhat intervals.
The nil Hecke ring and singularity of Schubert varieties.
The normality of closures of orbits in a Lie algebra.
The number of sides of a parallelogram.
The PBW filtration, Demazure modules and toroidal current algebras.