Scribbles

From OED Online, December 2020.

scribble, n. A quickly or carelessly composed piece of writing, esp. a letter or note; a worthless or trivial piece of writing. Also as a mass noun: quickly or carelessly composed writing. Often used depreciatively to refer to a person's own writing.

Also: musing, writing, decluttering, unraveling, straightening, practice, or what have you.

December 2020

For now just a massive and perplexing to-do list.

Schur-Weyl duality

From \((GL_m,S_n)\) duality to \((GL_m,GL_n)\) duality?

Bott-Samelson

Combinatorial characterization of equivariant multiplicity. Demazure operators. See entry on stable envelopes and MV cycles.

Shapovalov forms

What are they? What is it? From the dual Schur and Weyl modules, in the basis of MV cycles?

Loop groups and affine Grassmannians

Two \(\mathbb C^\times = \mathbb G_m(\mathbb C)\) actions. Modules for loop rotation.

Stable envelopes and MV cycles

Are they related? At least in type A.

Two actions agree

Soergel bimodules and \(H_T^\bullet(\textrm{Gr})\). See entry on Bott-Samelson. Make entry on equivariant cohomology.

The six functor formalism

For crying out loud.

Iwahori-Hecke algebras

Geometric, algebraic, and (?) combinatorial constructions of bases.

Gelfand-Tsetlin modules

Curious recursion.

Caldero-Chapoton formula

RTT Yangians and quantized shifted ones...are not related?