Andrews-Gordon type identities from combinations of Virasoro characters
Andrews-Gordon type identities from combinations of Virasoro characters
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DOI：
10.1007/s11139-006-9011-7
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发表时间：
2008-10-01
影响因子：
0.7
通讯作者：
Welsh, Trevor
中科院分区：
文献类型：
--
作者：
Feigin, Boris;Foda, Omar;Welsh, Trevor
对于p ∈ {3，4}和所有p' > p，p'与p互质，我们得到了Virasoro（W（2））特征标的chi（p，p '）（1，s）+ q（Delta）chi（p，p'）（p-1，s）组合的费米子表达式.将这些表达式与已知的乘积表达式等价，我们得到了类似于Andrews-Gordon恒等式的q-级数恒等式。对于p = 3，这些恒等式由Bytsko证明。对于p = 4，我们得到的恒等式的形式是p = 3情况下的恒等式的一种变化。（p，p '）=（3，14）的情形特别有趣，因为它不仅与W-2有关，而且与W-3特征标有关，并提供了原始Andrews-Gordon恒等式的W-3类似物。我们的费米表达式这些字符不同于安德鲁斯等人。其中涉及高斯多项式。
For p epsilon {3,4} and all p' > p, with p' coprime to p, we obtain fermionic expressions for the combination chi(p,p')(1,s) + q(Delta)chi (p,p')(p-1,s) of Virasoro (W (2)) characters for various values of s, and particular choices of Delta. Equating these expressions with known product expressions, we obtain q-series identities which are akin to the Andrews-Gordon identities. For p = 3, these identities were conjectured by Bytsko. For p = 4, we obtain identities whose form is a variation on that of the p = 3 cases. These identities appear to be new.The case (p,p') = (3,14) is particularly interesting because it relates not only to W-2, but also to W-3 characters, and offers W-3 analogues of the original Andrews-Gordon identities. Our fermionic expressions for these characters differ from those of Andrews et al. which involve Gaussian polynomials.