TY - JOUR
T1 - Andrews-Gordon type identities from combinations of Virasoro characters
AU - Feigin, Boris
AU - Foda, Omar
AU - Welsh, Trevor
PY - 2008/10
Y1 - 2008/10
N2 - For p ∈ {3,4} and all p′>p, with p′ coprime to p, we obtain fermionic expressions for the combination χ 1,s p,p′ +q Δ χ p-1,s p,p′ of Virasoro (W 2) characters for various values of s, and particular choices of Δ. 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.
AB - For p ∈ {3,4} and all p′>p, with p′ coprime to p, we obtain fermionic expressions for the combination χ 1,s p,p′ +q Δ χ p-1,s p,p′ of Virasoro (W 2) characters for various values of s, and particular choices of Δ. 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.
KW - Andrews-Gordon identities
KW - q-series identities
KW - Virasoro characters
UR - http://www.scopus.com/inward/record.url?scp=52649174905&partnerID=8YFLogxK
U2 - 10.1007/s11139-006-9011-7
DO - 10.1007/s11139-006-9011-7
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AN - SCOPUS:52649174905
SN - 1382-4090
VL - 17
SP - 33
EP - 52
JO - Ramanujan Journal
JF - Ramanujan Journal
IS - 1
ER -