Grassmannians and Representations

A survey of symmetric functions, Grassmannians, and representations of the unitary group

Framed Moduli and Grassmannians of Submodules

In this work we study a realization of moduli spaces of framed quiver representations as Grassmannians of submodules devised by Markus Reineke. Obtained is a generalization of this construction to finite dimensional associative algebras and for quivers with oriented cycles over an arbitrary infinite field. As an application we get an explicit realization of fibers for the moduli space bundle ov...

Hyperplane Sections of Grassmannians and the Number of MDS Linear Codes

We obtain some e!ective lower and upper bounds for the number of (n, k)-MDS linear codes over F q . As a consequence, one obtains an asymptotic formula for this number. These results also apply for the number of inequivalent representations over F q of the uniform matroid or, alternatively, the number of F q -rational points of certain open strata of Grassmannians. The techniques used in the de...

Lectures by Joel Kamnitzer

One can define an action of sl2 on a category to be a sequence of categories with functors between them satisfying certain relations. Such actions were studied by Chuang-Rouquier in the context of representations of the symmetric group in positive characteristic. They used this action to build an equivalence of categories which settled a case of Broue’s conjecture. Later, Cautis, Licata, and th...

From p-adic to real Grassmannians via the quantum

We interpolate between idempotents in the Hecke algebras associated with the Grassmann representation over different local fields. Consequently, we obtain a bijection between some irreducible representations geometrically defined for all local fields.