Search results for "symmetric group"
showing 10 items of 43 documents
Codimensions of algebras and growth functions
2008
Abstract Let A be an algebra over a field F of characteristic zero and let c n ( A ) , n = 1 , 2 , … , be its sequence of codimensions. We prove that if c n ( A ) is exponentially bounded, its exponential growth can be any real number >1. This is achieved by constructing, for any real number α > 1 , an F-algebra A α such that lim n → ∞ c n ( A α ) n exists and equals α. The methods are based on the representation theory of the symmetric group and on properties of infinite Sturmian and periodic words.
Catalan and Schröder permutations sortable by two restricted stacks
2020
Abstract Pattern avoiding machines were introduced recently by Claesson, Cerbai and Ferrari as a particular case of the two-stacks in series sorting device. They consist of two restricted stacks in series, ruled by a right-greedy procedure and the stacks avoid some specified patterns. Some of the obtained results have been further generalized to Cayley permutations by Cerbai, specialized to particular patterns by Defant and Zheng, or considered in the context of functions over the symmetric group by Berlow. In this work we study pattern avoiding machines where the first stack avoids a pair of patterns of length 3 and investigate those pairs for which sortable permutations are counted by the…
Cocharacters of Bilinear Mappings and Graded Matrices
2012
Let Mk(F) be the algebra of k ×k matrices over a field F of characteristic 0. If G is any group, we endow Mk(F) with the elementary grading induced by the k-tuple (1,...,1,g) where g ∈ G, g2 ≠ 1. Then the graded identities of Mk(F) depending only on variables of homogeneous degree g and g − 1 are obtained by a natural translation of the identities of bilinear mappings (see Bahturin and Drensky, Linear Algebra Appl 369:95–112, 2003). Here we study such identities by means of the representation theory of the symmetric group. We act with two copies of the symmetric group on a space of multilinear graded polynomials of homogeneous degree g and g − 1 and we find an explicit decomposition of the …
Calculating the Homology of the Image
2020
We introduce the alternating homology of a space with a symmetric group action, and give a new construction of the image computing spectral sequence (ICSS), which computes the homology of the image of a finite map from the alternating homology of its multiple point spaces. We illustrate and motivate the ICSS with simple examples.
Symmetric-group approach to the study of the traces ofp-order reduced-density operators and of products of these operators
1990
In this work we give the values of traces of p-order reduced-density operators. These traces are obtained by application of the spin functions and of the symmetric-group properties. The relations obtained here will allow an easy and fast evaluation of the high-order spin-adapted reduced Hamiltonian matrix elements and high-order Hamiltonian moments.
The Pauli Principle and Systems Consisting of Composite Particles
1993
In nature we often deal with many-body systems that are described in terms of particles that are not elementary but themselves composite. Examples of such composite particles are hadrons, atoms, phonons, and Cooper pairs. For the description of systems consisting of such composite particles in terms of the underlying degrees of freedom group theory plays an important role, in particular the symmetric group to describe the permutational symmetry of the wave function of the system, and unitary groups to describe the symmetry forced on the system by the interaction between the particles.
A characterization of fundamental algebras through S-characters
2020
Abstract Fundamental algebras play an important role in the theory of algebras with polynomial identities in characteristic zero. They are defined in terms of multialternating polynomials non vanishing on them. Here we give a characterization of fundamental algebras in terms of representations of symmetric groups obtaining this way an equivalent definition. As an application we determine when a finitely generated Grassmann algebra is fundamental.
Differential identities, 2 × 2 upper triangular matrices and varieties of almost polynomial growth
2019
Abstract We study the differential identities of the algebra U T 2 of 2 × 2 upper triangular matrices over a field of characteristic zero. We let the Lie algebra L = Der ( U T 2 ) of derivations of U T 2 (and its universal enveloping algebra) act on it. We study the space of multilinear differential identities in n variables as a module for the symmetric group S n and we determine the decomposition of the corresponding character into irreducibles. If V is the variety of differential algebras generated by U T 2 , we prove that unlike the other cases (ordinary identities, group graded identities) V does not have almost polynomial growth. Nevertheless we exhibit a subvariety U of V having almo…
Restricting irreducible characters to Sylow 𝑝-subgroups
2018
We restrict irreducible characters of finite groups of degree divisible by p p to their Sylow p p -subgroups and study the number of linear constituents.
Hyperspherical harmonic formalism for tetraquarks
2007
5 pages, 2 tables.-- ISI Article Identifier: 000250926800050.-- ArXiv pre-print available at: http://arxiv.org/abs/hep-ph/0610124