A simple definition for the universal Grassmannian order

A simple definition for the universal Grassmannian order

In this paper, we provide a combinatorial definition of the Universal Grassmannian order (or the Grassmannian Bruhat order) of Bergeron and Sottile. This defines the order in terms of inversions, and thus the order can be viewed as a generalization of the weak order for Coxeter groups. Finally, we use this understanding of the order to analyze the generating function of the number of elements a...

A Monoid for the Grassmannian Bruhat Order

Structure constants for the multiplication of Schubert polynomials by Schur symmetric polynomials are related to the enumeration of chains in a new partial order on S 1 , the Grassmaniann Bruhat order. Here we present a monoid M related to this order. We develop a notion of reduced sequences for M and show that M is analogous to the nil-Coxeter monoid for the weak order on S 1 .

Infinite - Genus Surfaces and the Universal Grassmannian

Correlation functions can be calculated on Riemann surfaces using the operator formalism. The state in the Hilbert space of the free field theory on the punctured disc, corresponding to the Riemann surface, is constructed at infinite genus, verifying the inclusion of these surfaces in the Grassmannian. In particular, a subset of the class of O HD surfaces can be identified with a subset of the ...

A simple construction of Grassmannian polylogarithms

The classical n-logarithm is a multivalued analytic function defined by induction as

Mani and shapur a universal faith for e universal kingdom