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Additional symmetries of constrained CKP and BKP hierarchies
The additional symmetries of the constrained CKP (cCKP) and BKP (cBKP)
hierarchies are given by their actions on the Lax operators, and their actions
on the eigenfunction and adjoint eigenfunction are
presented explicitly. Furthermore, we show that acting on the space of the wave
operator, forms new centerless and
-subalgebra of centerless respectively. In
order to define above symmetry flows of the cCKP and cBKP
hierarchies, two vital operators are introduced to revise the additional
symmetry flows of the CKP and BKP hierarchies.Comment: 14 pages, accepted by SCIENCE CHINA Mathematics(2010