The quantum analog of a symmetric pair: a construction in type (𝐶_{𝑛},𝐴₁×𝐶_{𝑛-1})

Baldoni, Welleda; Frajria, Pierluigi

doi:10.1090/S0002-9947-97-01759-5

The quantum analog of a symmetric pair: a construction in type $(C_n,A_1\times C_{n-1})$
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by Welleda Baldoni and Pierluigi Möseneder Frajria

Trans. Amer. Math. Soc. 349 (1997), 3235-3276

DOI: https://doi.org/10.1090/S0002-9947-97-01759-5

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Abstract:

Let $\mathcal {I}$ be the ideal in the enveloping algebra of $\mathfrak {sp}(n,\mathbb C)$ generated by the maximal compact subalgebra of $\mathfrak {sp}(n-1,1)$. In this paper we construct an analog of $\mathcal I$ in the quantized enveloping algebra $\mathcal {U}$ corresponding to a type $C_{n}$ diagram at generic $q$. We find generators for $\mathcal {I}$ and explicit bases for $\mathcal {U}/\mathcal {I}$.

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