m at h . Q A ] 6 A ug 1 99 8 Planscherel Measure on E q ( 2 )

ar X iv : m at h / 98 08 06 5 v 1 [ m at h . Q A ] 1 4 A ug 1 99 8 QUANTUM DETERMINANTS AND QUASIDETERMINANTS

ar X iv : 0 70 8 . 22 12 v 1 [ m at h . C O ] 1 6 A ug 2 00 7 Enumerative properties of NC ( B ) ( p , q )

We determine the rank generating function, the zeta polynomial and the Möbius function for the poset NC(p, q) of annular non-crossing partitions of type B, where p and q are two positive integers.

ar X iv : h ep - p h / 98 08 27 6 v 1 1 0 A ug 1 99 8 Superball dark matter 1

Supersymmetric models predict a natural dark-matter candidate , stable baryonic Q-balls. They could be copiously produced in the early Universe as a by-product of the Affleck-Dine baryogenesis. I review the cosmological and astrophysical implications , methods of detection, and the present limits on this form of dark matter.

m at h . Q A ] 1 9 A ug 1 99 8 Exterior Algebras Related to the Quantum Group O ( O q ( 3 ) )

For the 9-dimensional bicovariant differential calculi on the quantum group O(Oq(3)) several kinds of exterior algebras are examined. The corresponding dimensions, bicovariant subbimodules and eigenvalues of the antisymmetrizer are given. Exactly one of the exterior algebras studied by the authors has a unique left invariant form with maximal degree.

ar X iv : s ol v - in t / 9 80 80 16 v 1 2 6 A ug 1 99 8 Legendre transformations on the triangular lattice

Study of the nonlinear lattices ¨ q n = r(˙ q n)(g n+1 − g n), g n = g(q n − q n−1) (1) have brought Toda to the notion of dual system, which is obtained from the original one by " replacement of particles by springs and springs by particles accordingly to the certain rules " [1]. These rules are the following. The lattice (1) is equivalent to the Euler-Lagrange equations for the functional L =...