Block type symmetry of bigraded Toda Hierarchy

Abstract

In this paper, we define Orlov-Schulman's operators $M_L$, $M_R$, and then use them to construct the additional symmetries of the bigraded Toda hierarchy (BTH). We further show that these additional symmetries form an interesting infinite dimensional Lie algebra known as a Block type Lie algebra, whose structure theory and representation theory have recently received much attention in literature. By acting on two different spaces under the weak W-constraints we find in particular two representations of this Block type Lie algebra.

30 pages, accepted by Journal of Mathematical Physics

References in corpus (3)

• The Extended Bigraded Toda hierarchy
• On the BKP hierarchy: additional symmetries, Fay identity and Adler-Shiota-van Moerbeke formula
• Solutions of bigraded Toda hierarchy

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• Sato theory on the $q$-Toda hierarchy and its extension
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• Integrability on generalized $q$-Toda equation and hierarchy
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