Leading terms of relations for standard modules of the affine Lie algebras $C^{(1)}_n$

Authors: Mirko Primc, Tomislav Šikić

https://doi.org/10.1007/s11139-018-0052-5

Abstract: In this paper, we give a combinatorial parametrization of leading terms of defining relations for the vacuum level $k$ standard modules for the affine Lie algebra of type $C^{(1)}_n$ . Using this parametrization, we conjecture colored Rogers–Ramanujan type combinatorial identities for $<span id="MathJax-Element-3-Frame" class="MathJax" style="box-sizing: border-box; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 17px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>≥</mo><mn>2</mn></math>">n \geq 2$ and $k<span id="MathJax-Element-3-Frame" class="MathJax" style="box-sizing: border-box; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 17px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>≥</mo><mn>2</mn></math>"> \geq 2$ ; the identity in the case $n = k = 1$ is equivalent to one of Capparelli’s identities.

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