Representation Theory by Ian Grojnowski.

Interlude: The Philosophical lessons of “The Character Table Is Square”.

Coda: The Langlands Program.

Readings: “Local Representation Theory” and “Automorphic Forms, Representations and L-functions”.

Interesting scientific or quantitative thoughts or ideas!

Representation Theory by Ian Grojnowski.

Interlude: The Philosophical lessons of “The Character Table Is Square”.

Coda: The Langlands Program.

Readings: “Local Representation Theory” and “Automorphic Forms, Representations and L-functions”.

Representation Theory by Ian Grojnowski.

Noncompact Groups, Groups in Characteristic p and Lie Algebras.

IV.9 Representation Theory by Ian Grojnowski, Fourier Analysis: Pages 425 – 426.

Representation Theory by Ian Grojnowski.

Why Vector Spaces?

The number of partitions of n is about (1/4n√(3))e^{pÖ(2n/3)}.

Representation Theory by Ian Grojnowski.

Why Vector Spaces?

Theorem: Let G be a finite group. then the characters of the irreducible representations form an orthonormal basis of K-sub-G, the vector space of all complex valued functions on G that are constant functions on each conjugacy class. This means the character table is square.

Representation Theory by Ian Grojnowski.

Why Vector Spaces?

The analogy to Fourier transform decomposition.

Representation Theory by Ian Grojnowski.

Why Vector Spaces?

Definition: A representation of a group G on a vector space V is a homomorphism from G to GL(V). GL(V) is the set of linear maps from V to V.

If G is the dihedral group D_{8} acting on the set X of ordered pairs of vertices of the square, of which there are 16, then there are three orbits of G on X.

IV.8 Moduli Spaces by David. D. Ben-Zvi.

Invariants from moduli spaces.

Modular forms.

Further reading.

IV.9 Representation Theory by Ian Grojnowski.

Introduction.

Why vector spaces?

IV.8 Moduli Spaces by David. D. Ben-Zvi.

Moduli spaces and Jacobians.

Further directions.

Deformations and degenerations.

Moduli Spaces by David. D. Ben-Zvi.

Digression “Abstract Nonsense”.

Moduli spaces and representations.