Bosonic Formulas for \widehat{\mathfrak{s}\mathfrak{l}} 2 Coinvariants

We derive bosonic-type formulas for the characters of ₂ coinvariants.     

A Two-Parameter Deformed N = 2 SUSY Algebra

A two-parameter deformed N = 2 SUSY algebra is constructed by using the q-deformed bosonic and fermionic Newton oscillator algebras. The Fock space representation of the (q ₁,q ₂)-deformed N = 2 SUSY algebra is analyzed. The comparison between the algebra constructed and earlier versions of deformed N = 2 SUSY algebras is also made.     

Kontsevich and Takhtajan Construction of Star Product on the Poisson–Lie Group GL(2)

Comparing the star product defined by Takhtajan on the Poisson–Lie group GL(2) and any star product calculated from the Kontsevich's graphs (any K-star product) on the same group, we show, by direct computation, that the Takhtajan star product on GL(2) can't be written as a K-star product.     

Geometric lattice actions, entropy and fundamental groups

Let be a lattice in a noncompact simple Lie Group G, where . Suppose acts analytically and ergodically on a compact manifold M preserving a unimodular rigid geometric structure (e.g. a connection and a volume). We show that either the action is isometric or there exists a "large image" linear representation of . Under an additional assumption on the dynamics of the action, we associate to a virtual arithmetic quotient of full entropy. Received: December 14, 2000     

Analysis of an FRW cosmological model

The Einstein field equations for the Friedmann universe reduce to a system of three first-order equations for the space-like components and a constraint from the temporal component. We analyse the system from the viewpoints of symmetry and singularity analyses. The solutions of particular relevance to Cosmology are highlighted.      

En">Characters and Composition Factor Multiplicities for the Lie Superalgebra $${\mathfrak{g}}{\mathfrak{l}}$$ ( m / n )

The multiplicities a of simple modules L in the composition series of Kac modules V lambda for the Lie superalgebra (m/n ) were described by Serganova, leading to her solution of the character problem for (m/n ). In Serganova's algorithm all with nonzero a are determined for a given this algorithm, turns out to be rather complicated. In this Letter, a simple rule is conjectured to find all nonzero a for any given weight . In particular, we claim that for an r-fold atypical weight there are 2r distinct weights such that a = 1, and a = 0 for all other weights . Some related properties on the multiplicities a are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan–Lusztig polynomials is discussed.     

Invariant Differential Operators on Symmetric Cones and Hermitian Symmetric Spaces

We give a brief survey on the study of constructions of invariant differential operators on Riemannian symmetric spaces and of combinatorial and analytical properties of their eigenvalues, and pose some open questions.     

Symmetry Reductions of the Combined KdV—mKdV Equation

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无限维Heisenberg代数的导子代数和全形

给出了无维Ｈｅｉｓｒｂｅｒｇ代数的全形和全形的导子代数Ｄｅｒ（ｓ）证明（ｓ）不是一个完备李代数，但Ｄｅｒ（ｓ）是一个完备李代数。