Search results for "REPRESENTATION"
showing 10 items of 1710 documents
On the Asymptotics of Capelli Polynomials
2020
We present old and new results about Capelli polynomials, \(\mathbb {Z}_2\)-graded Capelli polynomials, Capelli polynomials with involution and their asymptotics.
On defects of characters and decomposition numbers
2017
We propose upper bounds for the number of modular constituents of the restriction modulo [math] of a complex irreducible character of a finite group, and for its decomposition numbers, in certain cases.
On the presence of families of pseudo-bosons in nilpotent Lie algebras of arbitrary corank
2019
We have recently shown that pseudo-bosonic operators realize concrete examples of finite dimensional nilpotent Lie algebras over the complex field. It has been the first time that such operators were analyzed in terms of nilpotent Lie algebras (under prescribed conditions of physical character). On the other hand, the general classification of a finite dimensional nilpotent Lie algebra $\mathfrak{l}$ may be given via the size of its Schur multiplier involving the so-called corank $t(\mathfrak{l})$ of $\mathfrak{l}$. We represent $\mathfrak{l}$ by pseudo-bosonic ladder operators for $t(\mathfrak{l}) \le 6$ and this allows us to represent $\mathfrak{l}$ when its dimension is $\le 5$.
Weights and Nilpotent Subgroups
2018
In a finite group G, we consider nilpotent weights, and prove a pi-version of the Alperin Weight Conjecture for certain pi-separable groups. This widely generalizes an earlier result by I. M. Isaacs and the first author.
Normed Quasi *-Algebras: Basic Theory and Examples
2020
In this chapter we shall consider the case, where \({\mathfrak A}\) is endowed with a norm topology, making \(({\mathfrak A},{{\mathfrak A}}_{\scriptscriptstyle 0})\) into a normed quasi *-algebra in the sense of Definition 3.1.1, below. This opens our discussion on locally convex quasi *-algebras, starting from the simplest situation. Nevertheless, as we shall see, simple does not mean trivial at all.
Representations of Finite Groups
2009
Dupin Cyclide Blends Between Quadric Surfaces for Shape Modeling
2004
We introduce a novel method to define Dupin cyclide blends between quadric primitives. Dupin cyclides are nonspherical algebraic surfaces discovered by French mathematician Pierre-Charles Dupin at the beginning of the 19th century. As a Dupin cyclide can be fully characterized by its principal circles, we have focussed our study on how to determine principal circles tangent to both quadrics being blended. This ensures that the Dupin cyclide we are constructing constitutes aG 1 blend. We use the Rational Quadratic Bezier Curve (RQBC) representation of circular arcs to model the principal circles, so the construction of each circle is reduced to the determination of the three control points o…
Representations of Affine Kac-Moody Algebras
1989
In the first chapter we explained how simple finite-dimensional Lie algebras can be completely characterized in terms of their Cartan matrices or Dynkin diagrams. The same holds for an arbitrary semisim-ple finite-dimensional Lie algebra. A semisimple Lie algebra is a direct sum of simple ideals which are pairwise orthogonal with respect to the Killing form. It follows that the Cartan matrix of a semisimple Lie algebra decomposes to a block diagonal form, each block representing a simple ideal. Similarly, the Dynkin diagram is a disconnected union of Dynkin diagrams of simple Lie algebras. Next we shall study certain infinite-dimensional Lie algebras which have many similarities with the si…
A construction of equivariant bundles on the space of symmetric forms
2021
We construct stable vector bundles on the space of symmetric forms of degree d in n+1 variables which are equivariant for the action of SL_{n+1}(C), and admit an equivariant free resolution of length 2. For n=1, we obtain new examples of stable vector bundles of rank d-1 on P^d, which are moreover equivariant for SL_2(C). The presentation matrix of these bundles attains Westwick's upper bound for the dimension of vector spaces of matrices of constant rank and fixed size.