We show that there is a kind of quantum group symmetry slq(2) in the usual Landau problem and it is this quantum group symmetry that governs the degeneracy of Landau levels. We find that under the periodic boundary condition, the degree of degeneracy of Landau levels is finite, and it just equals the dimension of the irreducible cyclic representation of the quantum group slq(2).

Let Cp denote the cyclic group of order p where p ≥ 3 is prime. We denote by V3 the indecomposable three dimensional representation of Cp over a field F of characteristic p. We compute a set of generators, in fact a SAGBI basis, for the ring of invariants F[V3 ⊕ V3]p . Our main result confirms the conjecture of Shank[15], for this example, that all modular rings of invariants of Cp are generate...

Let T be a split torus over local or global function field. The theory of BrylinskiDeligne gives rise to the metaplectic central extensions of T by a finite cyclic group. The representation theory of these metaplectic tori has been developed to some extent in the works of M. Weissman, G. Savin, W. T. Gan, P. McNamara and others. In this paper we propose a geometrization of this theory in the fr...

We discuss w ∞ and sl q (2) symmetries in multiple Chern-Simons theory on a torus. It is shown that these algebraic structures arise from the dynamics of the non-integrable phases of the Chern-Simons fields. The generators of these algebras are constructed from the Wilson line operators corresponding to these phases. The vacuum states form the basis of cyclic representation of sl q (2).

The metaplectic representation describes a class of automorphisms of the Heisenberg group H = H(G), defined for a locally compact abelian groupG. ForG = R ,H is the usual Heisenberg group. For the case when G is the finite cyclic group Zn, only partial constructions are known. Here we present new results for this case and we obtain an explicit construction of the metaplectic operators on C. We ...

Note. The determinant of a circulant matrix is an example of a group determinant, where the group is the cyclic group of order n. In 1880 Dedekind suggested generalizing the case of circulants (and more generally group de­ terminants for abelian groups) to arbitrary groups. It was this suggestion that led Frobenius to the creation group of representation theory. See [1] and the references therein.

We introduce a compressed de Bruijn representation of lambda terms and define its bijections to standard representations. Compact combinatorial generation algorithms are given for several families of lambda terms, including open, closed, simply typed and linear terms as well as type inference and normal order reduction algorithms. We specify our algorithms as a literate Prolog program. In the p...

We show that there exists quantum group symmetry slq(2) in the fractional quantum Hall effect (FQHE) and this symmetry governs the degeneracy of groundstate level. Under the periodic boundary condition, the degree of degeneracy is related to the cyclic representation of slq(2). We also discuss the influence of impurity by using quantum group technique and give the energy correction due to the i...

The efficient representation and manipulation of data is one of the fundamental tasks in the construction of large software systems. Parametric polymorphism has been one of the most successful approaches to date but, as of yet, has not been applicable to programming with quotient datatypes such as unordered pairs, cyclic lists, bags etc. This paper provides the basis for writing polymorphic pro...

As with most computer science problems, representation of the data is the key to ecient and eective solutions. Piecewise linear representation has been used for the representation of the data. This representation has been used by various researchers to support clustering, classication, indexing and association rule mining of time series data. A variety of algorithms have been proposed to obtain...