Functional analysis | Topological groups | Unitary representation theory | Permutation groups
The concept of system of imprimitivity is used in mathematics, particularly in algebra and analysis, both within the context of the theory of group representations. It was used by George Mackey as the basis for his theory of induced unitary representations of locally compact groups. The simplest case, and the context in which the idea was first noticed, is that of finite groups (see primitive permutation group). Consider a group G and subgroups H and K, with K contained in H. Then the left cosets of H in G are each the union of left cosets of K. Not only that, but translation (on one side) by any element g of G respects this decomposition. The connection with induced representations is that the permutation representation on cosets is the special case of induced representation, in which a representation is induced from a trivial representation. The structure, combinatorial in this case, respected by translation shows that either K is a maximal subgroup of G, or there is a system of imprimitivity (roughly, a lack of full "mixing"). In order to generalise this to other cases, the concept is re-expressed: first in terms of functions on G constant on K-cosets, and then in terms of projection operators (for example the averaging over K-cosets of elements of the group algebra). Mackey also used the idea for his explication of quantization theory based on preservation of relativity groups acting on configuration space. This generalized work of Eugene Wigner and others and is often considered to be one of the pioneering ideas in canonical quantization. (Wikipedia).
You should know what Impredicativity is.
In this video I discuss the concept of predicativity, impredicativity and vicious circles. The text for the video is found in https://gist.github.com/Nikolaj-K/aae1f4bd582e60e6b7e5b5431fee054c
From playlist Logic
On the Gross—Stark conjecture 1 by Mahesh Kakde
PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA
From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)
Simplifying expressions using the rules of exponents, quotient property
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From playlist Simplify Using the Rules of Exponents
Non-vanishing Theorems for the Gross Family of Elliptic Curves by Yukako Kezuka
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Thomas Dreyfus, Université de Strasbourg
May 17, Thomas Dreyfus, Université de Strasbourg Computing the difference Galois group of order 3 equations
From playlist Spring 2022 Online Kolchin seminar in Differential Algebra
Learn how to simplify an expression by applying the quotient rule of exponents
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From playlist Simplify Using the Rules of Exponents
Imprimitive irreducible representations of finite quasisimple groups by Gerhard Hiss
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Iwasawa Main Conjecture for Universal Families by Xin Wan
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Alexander HULPKE - Computational group theory, cohomology of groups and topological methods 2
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From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Using the reciprocal of a fraction to rewrite an expression with a positive power
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From playlist Simplify Using the Rules of Exponents
Applying the power rule of exponents to simplify an expression
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From playlist Simplify Using the Rules of Exponents
Galois groups of random integer polynomials - Manjul Bharğava
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From playlist Mathematics
on the Brumer-Stark Conjecture (Lecture 4) by Mahesh Kakde
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Applying the reciprocal rule with negative exponents to simplify an expression
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From playlist Simplify Using the Rules of Exponents
Simplify an expression using rules of exponents when the denominator has negative exponent
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Simplifying an expression using properties of exponents
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From playlist Simplify Using the Rules of Exponents | Quotient Rule
Learn the basics in simplifying an expression using the quotient rule of exponents
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From playlist Simplify Using the Rules of Exponents | Quotient Rule
Representation Theory(Repn Th) 2 by Gerhard Hiss
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From playlist Group Theory and Computational Methods
An Euler System for the Symmetric Square of a Modular Form - Chris Skinner
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From playlist Mathematics
Simplify rational expression using the rules of exponents
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From playlist Simplify Using the Rules of Exponents | Quotient Rule