Representation theory of Lie algebras
Let be the Weyl group of a semisimple Lie algebra (associate to fixed choice of a Cartan subalgebra ). Assume that a set of simple roots in is chosen. The affine action (also called the dot action) of the Weyl group on the space is where is the sum of all fundamental weights, or, equivalently, the half of the sum of all positive roots. (Wikipedia).
how to simplify an expression raised to a negative power
๐ Learn how to simplify expressions using the power rule and the negative exponent rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the p
From playlist Simplify Using the Rules of Exponents
Using the reciprocal of a fraction to rewrite an expression with a positive power
๐ Learn how to simplify expressions using the power rule and the negative exponent rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the p
From playlist Simplify Using the Rules of Exponents
How to apply the power to power rule with rational exponents
๐ Learn how to simplify rational powers using the power rule. There are some laws of exponents which might come handy when simplifying expressions with exponents. Some of the laws include the power rule which states that when an expression with an exponent is raised to another exponent tha
From playlist Raise an Exponent to a Fraction
How to apply the power to quotient rule to simplify an expression
๐ Learn how to simplify expressions using the power rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the parenthesis is multiplied to eac
From playlist Simplify Using the Rules of Exponents
How to simplify a fraction raised to a negative exponent
๐ Learn how to simplify expressions using the power rule and the negative exponent rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the p
From playlist Simplify Using the Rules of Exponents
Using the property of exponents to multiply expressions
๐ Learn how to simplify expressions using the power rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the parenthesis is multiplied to eac
From playlist Simplify Using the Rules of Exponents
Multiply an expression by applying product and power to product rule of exponents
๐ Learn how to simplify expressions using the power rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the parenthesis is multiplied to eac
From playlist Simplify Using the Rules of Exponents
Simplify an expression using rules of exponents when the denominator has negative exponent
๐ Learn how to simplify expressions using the power rule and the negative exponent rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the p
From playlist Simplify Using the Rules of Exponents
Applying the reciprocal rule with negative exponents to simplify an expression
๐ Learn how to simplify expressions using the power rule and the negative exponent rule of exponents. When several terms of an expression is raised to an exponent outside the parenthesis, the exponent is distributed over the individual terms in the expression and the exponent outside the p
From playlist Simplify Using the Rules of Exponents
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 Mรผnster)
David Rydh. Local structure of algebraic stacks and applications
Abstract: Some natural moduli problems, such as moduli of sheaves and moduli of singular curves, give rise to stacks with infinite stabilizers that are not known to be quotient stacks. The local structure theorem states that many stacks locally look like the quotient of a scheme by the act
From playlist CORONA GS
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 Nakajimaโs book `Lectures on Hilbert schemes of points on surfacesโ in a way that is accessible to PhD students interested in representa
From playlist SMRI Course: Hilbert Schemes
The Hecke category action on the principal block via Smith theory - Geordie Williamson
Geometric and Modular Representation Theory Seminar Topic: The Hecke category action on the principal block via Smith theory Speaker: Geordie Williamson Affiliation: University of Sydney; Distinguished Visiting Professor, School of Mathematics Date: January 27, 2021 For more video please
From playlist Geordie Williamson external seminars
The center of the small quantum group - Pablo Boixeda Alvarez
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: The center of the small quantum group Speaker: Pablo Boixeda Alvarez Affiliation: Member, School of Mathematics Date: November 17, 2020 For more video please visit http://video.ias.edu
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Gopal Prasad: Descent in Bruhat-Tits theory
Bruhat-Tits theory applies to a semisimple group G, defined over an henselian discretly valued field K, such that G admits a Borel K-subgroup after an extension of K. The construction of the theory goes then by a deep Galois descent argument for the building and also for the parahoric grou
From playlist Algebraic and Complex Geometry
Laura Rider: Modular Perverse Sheaves on the affine Flag Variety
There are two categorical realizations of the affine Hecke algebra: constructible sheaves on the affine flag variety and coherent sheaves on the Langlands dual Steinberg variety. A fundamental problem in geometric representation theory is to relate these two categories by a category equiva
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Dynamics on character varieties - William Goldman
Character Varieties, Dynamics and Arithmetic Topic: Dynamics on character varieties Speaker: William Goldman Affiliation: University of Maryland; Member, School of Mathematics Date: November 17, 2021 In these two talks, I will describe how the classification of locally homogeneous geomet
From playlist Mathematics
Joel Kamnitzer: Categorical g-actions for modules over truncated shifted Yangians
CIRM VIRTUAL CONFERENCE Given a representation V of a reductive group G, Braverman-Finkelberg-Nakajima defined a Poisson variety called the Coulomb branch, using a convolution algebra construction. This variety comes with a natural deformation quantization, called a Coulomb branch algebr
From playlist Virtual Conference
Learn how to apply the power rule with fractional powers
๐ Learn how to simplify rational powers using the power rule. There are some laws of exponents which might come handy when simplifying expressions with exponents. Some of the laws include the power rule which states that when an expression with an exponent is raised to another exponent tha
From playlist Raise an Exponent to a Fraction
Holomorphic rigid geometric structures on compact manifolds by Sorin Dumitrescu
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles