Reflection groups | Permutation groups | Coxeter groups | Symmetry | Representation theory
The affine symmetric groups are a family of mathematical structures that describe the symmetries of the number line and the regular triangular tiling of the plane, as well as related higher-dimensional objects. Each one is an infinite extension of a finite symmetric group, the group of permutations (rearrangements) of a finite set. In addition to their geometric description, the affine symmetric groups may be defined as collections of permutations of the integers (..., −2, −1, 0, 1, 2, ...) that are periodic in a certain sense, or in purely algebraic terms as a group with certain generators and relations. They are studied as part of the fields of combinatorics and representation theory. Many important combinatorial properties of the finite symmetric groups can be extended to affine symmetric groups. Permutation statistics such as descents and inversions can be defined in the affine case. As in the finite case, the natural combinatorial definitions for these statistics also have a geometric interpretation. The affine symmetric groups have close relationships with other mathematical objects, including juggling patterns and certain complex reflection groups. Many of their combinatorial and geometric properties extend to the broader family of affine Coxeter groups. (Wikipedia).
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
In this video we construct a symmetric group from the set that contains the six permutations of a 3 element group under composition of mappings as our binary operation. The specifics topics in this video include: permutations, sets, groups, injective, surjective, bijective mappings, onto
From playlist Abstract algebra
Definition of the Symmetric Group
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of the Symmetric Group
From playlist Abstract Algebra
Permutation Groups and Symmetric Groups | Abstract Algebra
We introduce permutation groups and symmetric groups. We cover some permutation notation, composition of permutations, composition of functions in general, and prove that the permutations of a set make a group (with certain details omitted). #abstractalgebra #grouptheory We will see the
From playlist Abstract Algebra
Group theory 22: Symmetric groups
This lecture is part of an online mathematics course on group theory. It covers the basic theory of symmetric and alternating groups, in particular their conjugacy classes.
From playlist Group theory
Visual Group Theory, Lecture 2.3: Symmetric and alternating groups
Visual Group Theory, Lecture 2.3: Symmetric and alternating groups In this lecture, we introduce the last two of our "5 families" of groups: (4) symmetric groups and (5) alternating groups. The symmetric group S_n is the group of all n! permutations of {1,...,n}. We see several different
From playlist Visual Group Theory
algebraic geometry 5 Affine space and the Zariski topology
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of affine space and its Zariski topology.
From playlist Algebraic geometry I: Varieties
Symmetric matrices - eigenvalues & eigenvectors
Free ebook http://tinyurl.com/EngMathYT A basic introduction to symmetric matrices and their properties, including eigenvalues and eigenvectors. Several examples are presented to illustrate the ideas. Symmetric matrices enjoy interesting applications to quadratic forms.
From playlist Engineering Mathematics
Representations of affine Lie algebras vs quantum groups: fusion, factorization and E_2...- Lin Chen
Short Talks by Postdoctoral Members Topic: Representations of affine Lie algebras vs quantum groups: fusion, factorization and E_2 structures Speaker: Lin Chen Affiliation: Member, School of Mathematics Date: September 22, 2021
From playlist Mathematics
Group Theory for Cryptology by Carlo Scoppola
PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund
From playlist Group Algebras, Representations And Computation
Anthony Henderson: Hilbert Schemes Lecture 1
SMRI Seminar Series: 'Hilbert Schemes' Lecture 1 Introduction Anthony Henderson (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students interested in representa
From playlist SMRI Course: Hilbert Schemes
Kevin Coulembier: Frobenius exact tensor categories
Abstract: Partly motivated by Grothendieck’s original vision for motives, the question arises of when a tensor category (k-linear symmetric monoidal rigid abelian category) is tannakian, i.e. is the representation category of an affine group scheme, or more generally of a groupoid in schem
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
Path isomorphisms between quiver Hecke and diagrammatic Bott-Samelson endomorphism... - Amit Hazi
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Path isomorphisms between quiver Hecke and diagrammatic Bott-Samelson endomorphism algebras Speaker: Amit Hazi Affiliation: University of London Date: November 17, 2020 For more video please visit http://vi
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Coulomb Branches for Quiver Gauge Theories With Symmetrizers by Alex Weekes
PROGRAM QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pandi
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Frobenius exact symmetric tensor categories - Pavel Etingof
Geometric and Modular Representation Theory Seminar Topic: Frobenius exact symmetric tensor categories Speaker: Pavel Etingof Affiliation: Massachusetts Institute of Technology Date: May 12, 2021 For more video please visit https://www.ias.edu/video
From playlist Seminar on Geometric and Modular Representation Theory
Anthony Henderson: Hilbert Schemes Lecture 4
SMRI Seminar Series: 'Hilbert Schemes' Lecture 4 Kleinian singularities 1 Anthony Henderson (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students interested i
From playlist SMRI Course: Hilbert Schemes
Robert Cass: Perverse mod p sheaves on the affine Grassmannian
28 September 2021 Abstract: The geometric Satake equivalence relates representations of a reductive group to perverse sheaves on an affine Grassmannian. Depending on the intended application, there are several versions of this equivalence for different sheaf theories and versions of the a
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
David Ben-Zvi: Geometric Langlands correspondence and topological field theory - Part 2
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
The General Linear Group, The Special Linear Group, The Group C^n with Componentwise Multiplication
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The General Linear Group, The Special Linear Group, The Group C^n with Componentwise Multiplication
From playlist Abstract Algebra
Monica Vazirani: Representations of the affine BMW category
The BMW algebra is a deformation of the Brauer algebra, and has the Hecke algebra of type A as a quotient. Its specializations play a role in types B, C, D akin to that of the symmetric group in Schur-Weyl duality. I will discuss Walker’s TQFT-motivated 1-handle construction of a family of
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification