[Todos] Coloquios del Departamento de Matemática

[Daniel Carando]

Próximo Coloquio:
Jueves 3 de julio a las 16:00, Aula E24

Laurent Rigal
Université de Saint-Etienne

Prime ideals in the quantum grassmannian.


The theory of quantum groups and algebras provides very natural non
commutative analogues of rings of coordinates on very interesting
varieties such as the grassmannian and its Schubert subvarieties. The
non commutative structure of these algebras encode interesting
features of the classical varieties they deform.

In this talk, I will introduce the quantum analogues of the coordinate
ring of the grassmannian and of its Schubert subvarieties. I will show
how a convenient use of the quantum analogues of the coordinate ring
of Schubert varieties allows a fairly precise description of the prime
ideals of the ''quantum grassmannian'' invariant under the action of a
natural torus $H$.

This approach leads to a very stricking parameterisation of the
$H$-invariant prime ideals in the ''quantum grassmannian''. The
interesting point here is that this parameterisation shows a strong
link between the quantum setting and very recent combinatorial
developements in the study of the so-called totally positive
grassmannian. I will also describe this link.

All this is joint work with S. Launois and T.H. Lenagan.



Están todos cordialmente invitados!

Daniel Carando


http://mate.dm.uba.ar/~dcarando/coloquios/