See: Symmetric group representations, General linear group representations

Videos

- A gentle introduction to group representation theory -Peter Buergisser
- Google: symmetric group general linear group representation theory
- Google: representation theory
- Google: representation theory symmetric group
- Google: representation theory general linear group
- Google: Schur Weyl duality

Texts

- Groups and Representation Theory by Kevin McGerty
- Slides: Group Representations and Symmetric Functions by Bruce Sagan
- Book: "The Symmetric Group: Representations, Combinatorial Algorithms and Symmetric Functions" by Bruce Sagan

Wikipedia

Think about commutativity and noncommutativity, the exterior algebra.

Think about (A-B)^n. This relates to the Euler characteristic.

Elements of a noncyclic group can't be mapped to corresponding roots of unity if there are elements whose orders are relatively prime. For then you could combine the two roots of unity to get a generator that is a product of the two orders.

Open problem: Calculating plethysm.

What do we know about matrices whose power to some N equals 1? Then the power symmetric function equals ... ? And the other symmetric functions of the eigenvalues...?

What can we say about the representation theory of Coxeter groups?

Parsiųstas iš http://www.ms.lt/sodas/Book/RepresentationTheory

Puslapis paskutinį kartą pakeistas 2019 vasario 05 d., 12:57