On the law of large numbers for Demazure modules of sl2hat

TL;DR

This paper establishes a weak law of large numbers for weight distributions in level 1 Demazure modules of sl2hat, providing insights into their asymptotic behavior and conjecturing similar properties for broader classes.

Contribution

It determines the covariance of weight distributions and proves a weak law of large numbers for level 1 Demazure modules of sl2hat, advancing understanding of their asymptotic properties.

Findings

Covariance of weight distribution determined

Weak law of large numbers proved for level 1 modules

Conjecture proposed for general Demazure modules

Abstract

We determine the covariance of the weight distribution in level 1 Demazure modules of sl2hat. This allows us to prove a weak law of large numbers for these weight distributions, and leads to a conjecture about the asymptotic concentration of weights for arbitrary Demazure modules.