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A Deformed Quon Algebra

Hery Randriamaro (2019)

Communications in Mathematics

The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators obey the quon algebra which interpolates between fermions and bosons. In this paper we generalize these models by introducing a deformation of the quon algebra generated by a collection of operators a i , k , ( i , k ) * × [ m ] , on an infinite dimensional vector space satisfying the...

A Pieri-type formula for even orthogonal Grassmannians

Piotr Pragacz, Jan Ratajski (2003)

Fundamenta Mathematicae

We study the cohomology ring of the Grassmannian G of isotropic n-subspaces of a complex 2m-dimensional vector space, endowed with a nondegenerate orthogonal form (here 1 ≤ n < m). We state and prove a formula giving the Schubert class decomposition of the cohomology products in H*(G) of general Schubert classes by "special Schubert classes", i.e. the Chern classes of the dual of the tautological vector bundle of rank n on G. We discuss some related properties of reduced decompositions of "barred...

A quantitative aspect of non-unique factorizations: the Narkiewicz constants II

Weidong Gao, Yuanlin Li, Jiangtao Peng (2011)

Colloquium Mathematicae

Let K be an algebraic number field with non-trivial class group G and K be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let F k ( x ) denote the number of non-zero principal ideals a K with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that F k ( x ) behaves, for x → ∞, asymptotically like x ( l o g x ) 1 / | G | - 1 ( l o g l o g x ) k ( G ) . In this article, it is proved that for every prime p, ( C p C p ) = 2 p , and it is also proved that ( C m p C m p ) = 2 m p if ( C m C m ) = 2 m and m is large enough. In particular, it is shown that for...

Boolean differential operators

Jorge Catumba, Rafael Díaz (2014)

Commentationes Mathematicae Universitatis Carolinae

We consider four combinatorial interpretations for the algebra of Boolean differential operators and construct, for each interpretation, a matrix representation for the algebra of Boolean differential operators.

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