VI-modules in nondescribing characteristic, part I

Characteristic Classes and Fredholm Modules

We derive simple explicit formula for the character of a cycle in the Connes’ (b, B)-bicomplex of cyclic cohomology and apply it to write formulas for the equivariant Chern character and characters of finitely-summable bounded Fredholm modules.

Math 101a: Algebra I Part B: Rings and Modules

In the unit on rings, I explained category theory and general rings at the same time. Then I talked mostly about commutative rings. In the unit on modules, I again mixed category theory into the basic notions and progressed to the structure theorem for finitely generated modules over PID’s. Jordan canonical forms were used as an application. The uniqueness part of the structure theorem was put ...

Homomorphisms between Verma Modules in Characteristic P

Let g be a complex semisimple Lie algebra, with a Bore1 subalgebra b c g and Cartan subalgebra h c b. In classifying the finite dimensional representations of g, Cartan showed that any simple finite dimensional g-module has a generating element u, annihilated by n = [b, b], on which h acts by a linear form I E h*. Such an element is called a primitive vector (for the module). Harish-Chandra [9]...

The Irreducible Specht Modules in Characteristic 2

In the representation theory of nite groups it is useful to know which ordinary irreducible representations remain irreducible modulo a prime p. For the symmetric groups S n this amounts to determining which Specht modules are irreducible over a eld of characteristic p. Throughout this note we work in characteristic 2, and in this case we classify the irreducible Specht modules, thereby verifyi...

Hæmatological Technique. Part VI