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suppose we have a map $f:\mathbb{Z}\longrightarrow\mathbb{C}[t^{\pm}]$ with property that $f(i)=-f(-i)$.

The algebra $\mathcal{T}=\mathbb{C}[t^{\pm}][L^{\pm},M^{\pm}]/[LM=tML]$ acts on $f$ by $(Lf)(i)=f(i+1),(Mf)(i)=t^if(i)$.

Should the annihilating ideal of $f$ generated by annihilators in symmetric part of $\mathcal{T}$?

Symmetric part means the subset with all element like $aL^xM^y+aL^{-x}M^{-y}$ and their multiplication or linear combination.


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Is this question too hard? I do not have any good idea yet. –  Xuanting Cai Apr 26 '11 at 19:36
The question is incomprehensible. Do you mean "Is" instead of "Should"? What does ${\bf C}[t^{\pm}]$ mean? –  Gerry Myerson May 8 '11 at 23:42
OP seems to have abandoned this question. Voting to close. –  Gerry Myerson May 11 '11 at 6:07
C[t^{\pm}] means the Laurant Polynomials of t –  Xuanting Cai May 28 '11 at 22:18
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