Ideals Generated by Traces or by Supertraces in the Symplectic Reflection Algebra H_1, _V (I₂(2m + 1)) II

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Abstract: The algebra

m a t h c a l H : = H_{1, u} (I_{2} (2 m + 1))

of observables of the Calogero model based on the root system

I_{2} (2 m + 1)

has an

m

-dimensional space of traces and an

(m + 1)

-dimensional space of supertraces. In the preceding paper we found all values of the parameter

u

for which either the space of traces contains a~degenerate nonzero trace

t r_{u}

or the space of supertraces contains a~degenerate nonzero supertrace

s t r_{u}

and, as a~consequence, the algebra

m a t h c a l H

has two-sided ideals: one consisting of all vectors in the kernel of the form

B_{t r_{u}} (x, y) = t r_{u} (x y)

or another consisting of all vectors in the kernel of the form

B_{s t r_{u}} (x, y) = s t r_{u} (x y)

. We noticed that if

u = f r a c z 2 m + 1

, where

z i n m a t h b b Z s e t m i n u s (2 m + 1) m a t h b b Z

, then there exist both a degenerate trace and a~degenerate supertrace on

m a t h c a l H

. Here we prove that the ideals determined by these degenerate forms coincide.

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Ideals Generated by Traces or by Supertraces in the Symplectic Reflection Algebra H1, V (I2(2m + 1)) II