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Schedule

DateSpeakerDetails
Sep. 29, 2019. 19:15
Preliminary meeting. Selection of a seminar topic, administrative details, etc.
Oct. 10, 2019. 20:30Devkota, Prabhat

Rudiments of Lie Groups. Lie algebra of a lie group, exponential mapping and adjoint representation. Discussion of su(2) and sl(2).

References: You can find notes here.

Oct. 18, 2019. 19:30

Representations and Irreducibility. Representations of lie groups and algebras, sub-representations, irreducible representations, common operations (direct sum, tensor product, etc), intertwining operators, and proof of Schur's lemma.

References: See Sections 4.1 to 4.4 in Alexander Kirillov's notes. For a review of common linear-algebraic constructions refer to Appendix B in Fulton and Harris' "Representation Theory: A First Course"

Oct. 25, 2019.
No meeting.
Nov. 1, 2019.

Young diagrams. Young diagrams and their connections with the representation theory of the symmetric groups and the simpler Lie algebras.

References: See Appendix A of Lando's Graphs on Surfaces and their Applications for a quick overview (also here). Chapters 1-2 of Serre's Linear Representations of Finite Groups are also useful.

Nov. 8, 2019

First look at the classification of connected Abelian Lie groups and connected complex Abelian Lie groups.

References: The notes can be found here.

Nov 15, 2019Aryal, Deepak

Killing form, solvable, nilpotent and semi-simple lie algebras, existence of maximal solvable and nilpotent radical, equivalent definitions of semisimple lie algebras (in terms of killing form and direct sum of simple lie algebra).

References: Page 88-90 and 95-98 of the book "Lie Groups: An approach through invariants and representations" by Claudio Procesi.

Nov 22, 2019

Introduction to Root Systems and Dynkin diagrams: First steps of classifying Lie Algebras geometrically.

  • Cartan subalgebras, root sets, dual of Cartan subalgebras, root systems, Dynkin diagrams.

References: Fulton and Harris, Part IV section 21.1Frederic Schuller - Classification of Lie algebras and Dynkin diagrams

Nov 29, 2019Oprea, Maria AntoniaRepresentations of sl(2, C)
Dec 28, 2019Devkota, PrabhatThe Levi-Malcev theorem
Jan. 11, 2020Pal, Abhik

Classification theorem of semisimple Lie Algebras.

References: Humphreys "Introduction to Lie Algebra and Representation Theory" Part 3 sections 9-11.

19:00. Jan. 19, 2020Lie's theorem and Lie-Kolchin theorem

General Information

Meeting time, location

19:30. Room 120 (Seminar Room), Research 1


Participants

Pal, AbhikAryal, Deepak Irungu, Martin Waiharo Falkenburg, Pia Cosma Devkota, Prabhat Blloshmi, Denida Mele, Crystal Oprea, Maria Antonia

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