scholarly journals Generators and relations for Schur algebras

2001 ◽  
Vol 7 (8) ◽  
pp. 54-62 ◽  
Author(s):  
Stephen Doty ◽  
Anthony Giaquinto
Keyword(s):  
Schur Algebras ◽  
Generators And Relations

Cellular bases of generalised q-Schur algebras

2016 ◽  
Vol 162 (3) ◽  
pp. 533-560
Author(s):  
STEPHEN DOTY ◽  
ANTHONY GIAQUINTO
Keyword(s):  
Representation Theory ◽  
Finite Type ◽  
Basic Structure ◽  
Schur Algebras ◽  
Generators And Relations

AbstractStarting from their defining presentation by generators and relations, we develop the basic structure and representation theory of generalised q-Schur algebras of finite type.

Presenting Little q-Schur Algebras uk(2; r)

2017 ◽  
Vol 24 (02) ◽  
pp. 297-308
Author(s):  
Zhihao Bian ◽  
Mingqiang Liu
Keyword(s):  
Quantum Groups ◽  
Schur Algebras ◽  
Du Fu ◽  
Generators And Relations

Little q-Schur algebras were introduced as homomorphic images of the infinitesimal quantum groups by Du, Fu and Wang. In this paper, we obtain a presentation by generators and relations for little q-Schur algebras uk(2, r).

Presenting integral q-Schur algebras

2019 ◽  
Vol 30 (01) ◽  
pp. 1950002
Author(s):  
Qiang Fu ◽  
Wenting Gao
Keyword(s):  
Integral Formula ◽  
Integral Form ◽  
Algebra Homomorphism ◽  
Schur Algebras ◽  
Generating Set ◽  
Generators And Relations ◽  
Schur Algebra

Let [Formula: see text] be the Lusztig integral form of quantum [Formula: see text]. There is a natural surjective algebra homomorphism [Formula: see text] from [Formula: see text] to the integral [Formula: see text]-Schur algebra [Formula: see text]. We give a generating set for the kernel of [Formula: see text]. In particular, we obtain a presentation of the [Formula: see text]-Schur algebra by generators and relations over any field.

scholarly journals Quiver origami: discrete gauging and folding

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Antoine Bourget ◽  
Amihay Hanany ◽  
Dominik Miketa
Keyword(s):  
Gauge Theories ◽  
Generators And Relations

Abstract We study two types of discrete operations on Coulomb branches of 3d$$ \mathcal{N} $$ N = 4 quiver gauge theories using both abelianisation and the monopole formula. We generalise previous work on discrete quotients of Coulomb branches and introduce novel wreathed quiver theories. We further study quiver folding which produces Coulomb branches of non-simply laced quivers. Our methods explicitly describe Coulomb branches in terms of generators and relations including mass deformations.

scholarly journals Dominant and global dimension of blocks of quantised Schur algebras

2021 ◽  
Author(s):  
Ming Fang ◽  
Wei Hu ◽  
Steffen Koenig
Keyword(s):  
Hecke Algebras ◽  
Symmetric Groups ◽  
Global Dimension ◽  
Group Algebras ◽  
Dominant Dimension ◽  
Schur Algebras ◽  
Homological Dimensions ◽  
Weyl Duality

AbstractGroup algebras of symmetric groups and their Hecke algebras are in Schur-Weyl duality with classical and quantised Schur algebras, respectively. Two homological dimensions, the dominant dimension and the global dimension, of the indecomposable summands (blocks) of these Schur algebras S(n, r) and $$S_q(n,r)$$ S q ( n , r ) with $$n \geqslant r$$ n ⩾ r are determined explicitly, using a result on derived invariance in Fang, Hu and Koenig (J Reine Angew Math 770:59–85, 2021).

scholarly journals Exponent Reduction for Projective Schur Algebras

2001 ◽  
Vol 239 (1) ◽  
pp. 356-364 ◽  
Author(s):  
Eli Aljadeff ◽  
Jack Sonn
Keyword(s):  
Schur Algebras

scholarly journals REGULAR FUNCTIONS ON THE SHILOV BOUNDARY

2005 ◽  
Vol 04 (06) ◽  
pp. 613-629 ◽  
Author(s):  
OLGA BERSHTEIN
Keyword(s):  
Symmetric Domain ◽  
Principal Series ◽  
Bounded Symmetric Domain ◽  
Bounded Symmetric Domains ◽  
Shilov Boundary ◽  
Generators And Relations ◽  
Regular Functions ◽  
Degenerate Principal Series

In this paper a *-algebra of regular functions on the Shilov boundary S(𝔻) of bounded symmetric domain 𝔻 is constructed. The algebras of regular functions on S(𝔻) are described in terms of generators and relations for two particular series of bounded symmetric domains. Also, the degenerate principal series of quantum Harish–Chandra modules related to S(𝔻) = Un is investigated.

On multiplicative systems defined by generators and relations

1953 ◽  
Vol 49 (4) ◽  
pp. 579-589 ◽  
Author(s):  
Trevor Evans
Keyword(s):  
Automorphism Group ◽  
Finite Number ◽  
Cyclic Group ◽  
Complete Information ◽  
Isomorphism Problem ◽  
Infinite Cyclic Group ◽  
Generators And Relations ◽  
Decision Method ◽  
Multiplicative Systems ◽  
Finitely Related

The techniques developed in (9) are used here to study the properties of multiplicative systems generated by one element (monogenie systems). The results are of two kinds. First, we obtain fairly complete information about the automorphisms and endo-morphisms of free and finitely related loops. The automorphism group of the free monogenie loop is the infinite cyclic group, each automorphism being obtained by mapping the generator on one of its repeated inverses. A monogenie loop with a finite, non-empty set of relations has only a finite number of endomorphisms. These are obtained by mapping the generator on some of the components, or their repeated inverses, occurring in the relations. We use the same methods to solve the isomorphism problem for monogenie loops, i.e. we give a method for determining whether two finitely related monogenie loops are isomorphic. The decision method consists essentially of constructing all homomorphisms between two given finitely related monogenie loops.

LORENTZ COVARIANCE FOR THE QUANTUM ALGEBRA OF OBSERVABLES: NAMBU–GOTO STRINGS IN 3 + 1 DIMENSIONS

2002 ◽  
Vol 17 (17) ◽  
pp. 2331-2349 ◽  
Author(s):  
GERRIT HANDRICH
Keyword(s):  
Rest Frame ◽  
Poisson Algebra ◽  
Quantum Algebra ◽  
Substantial Part ◽  
Quantum Case ◽  
Generators And Relations ◽  
Defining Relations ◽  
Algebra Of Observables ◽  
The One ◽  
The Relationship

To postulate correspondence for the observables only is a promising approach to a fully satisfying quantization of the Nambu–Goto string. The relationship between the Poisson algebra of observables and the corresponding quantum algebra is established in the language of generators and relations. A very valuable tool is the transformation to the string's rest frame, since a substantial part of the relations are solved. It is the aim of this paper to clarify the relationship between the fully covariant and the rest frame description. Both in the classical and in the quantum case, an efficient method for recovering the covariant algebra from the one in the rest frame is described. Restrictions on the quantum defining relations are obtained, which are not taken into account when one postulates correspondence for the rest frame algebra. For the part of the algebra studied up to now in explicit computations, these further restrictions alone determine the quantum algebra uniquely — in full consistency with the further restrictions found in the rest frame.

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