Solution of Contraction Equations for the Pauli Grading of sl(3,C)
We consider the Pauli grading of the Lie algebra sl(3,C) and use a concept of graded contractions to construct non-isomorphic
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Z_2^n grading of the classical Lie algebras
The Z_2^n gradings of the classical Lie algebras are described. To elucidate the grading, the classical Lie algebras are expressed
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Cohomology on Toric Varieties and Local Cohomology with Monomial Supports
We study the local cohomology modules H^i_B(R) for a reduced monomial ideal B in a polynomial ring R=k[X_1,...,X_n]. We consider
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On Some Integrable Generalisations of the Continuous Toda System
In the present paper we obtain some integrable generalisations of the continuous Toda system generated by a flat connection form
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An Algebraic Duality Theory for Multiplicative Unitaries
Multiplicative Unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated
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Bosonization, soliton-particle duality and Mandelstam-Halpern operators
The generalized massive Thirring model (GMT) with $N_{f}$[=number of positive roots of $su(n)$] fermion species is bosonized in the context
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Extended Conformal Symmetry
We show that the grading of fields by conformal weight, when built into the initial group symmetry, provides a discrete,
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Nonabelian Toda equations associated with classical Lie groups
The grading operators for all nonequivalent Z-gradations of classical Lie algebras are represented in the explicit block matrix form. The
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Non Abelian Toda models and Constrained KP hierarchies
A general construction of affine Non Abelian Toda models in terms of gauged two loop WZNW model is discussed. Its
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On the Embedding of Space-Time Symmetries into Simple Superalgebras
We explore the embedding of Spin groups of arbitrary dimension and signature into simple superalgebras in the case of extended
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Representation theory of a W-algebra from generalised DS reduction
We investigate the W-algebra resulting from Drinfel'd-Sokolov reduction of a $B_2$ WZW model with respect to the grading induced by
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Stability Conditions For Topological D-branes: A Worldsheet Approach
We study conditions on the topological D-branes of types A and B obtained by requiring a proper matching of the
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Supersymmetry and Homotopy
The homotopical information hidden in a supersymmetric structure is revealed by considering deformations of a configuration manifold. This is in
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The exactly integrable systems connected with semisimple algebras of the second rank $A_2,B_2,C_2,G_2$
All exactly integrable systems connected with the semisimple algebras of the second rank with an arbitrary choice of the grading
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The exterior algebra and `Spin' of an orthogonal g-module
A well-known result of Kostant gives a description of the G-module structure for the exterior algebra of Lie algebra $\frak
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The non chiral fusion rules in rational conformal field theories
We introduce a general method in order to construct the non chiral fusion rules which determine the operator content of
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Topology and Quantization
A simple algebraic model for charged particle moving in two dimensional space under influence of singular magnetic field is given.
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