Basic Representations of A_{2l}^(2) and D_{l+1}^(2) and the Polynomial Solutions to the Reduced BKP Hierarchies

TL;DR

This paper explores the basic representations of certain affine Lie algebras, expressing weight vectors via Schur's Q-functions, and introduces a novel method for obtaining polynomial solutions to reduced BKP hierarchies using a Maya game rule.

Contribution

It provides a new approach to represent affine Lie algebra weights and links polynomial solutions of BKP hierarchies to combinatorial Maya game rules.

Findings

Representation of weight vectors using Schur's Q-functions.

A method to generate polynomial solutions via Maya game.

Connection between algebra representations and combinatorial rules.

Abstract

Basic representations of A_{2l}^(2) and D_{l+1}^(2) are studied. The weight vectors are represented in terms of Schur's $Q$-functions. The method to get the polynomial solutions to the reduced BKP hierarchies is shown to be equivalent to a certain rule in Maya game.