Speaker: Junichi Shiraishi (University of Tokyo)
Abstract: We introduce a unital associative algebra,
(1) having two complex parameters ($q$ and $k$),
(2) generated by a certain set of generators ($K^\pm_m$ ($\pm m\geq
0$), $T_m$ ($m\in \mathbb{Z}$), and $G^\pm_m$
($m\in \mathbb{Z}+{1\over 2}$ in the Neveu-Schwarz sector,
$m\in \mathbb{Z}$ in the Ramond sector), and (3) satisfying relations
which are at most quartic.
Brute force calculations of some low-lying Kac determinants are made,
providing us with a conjecture for the factorization property of the
Kac determinants in general. It is shown that by taking the conformal
limit ($q\rightarrow 1$) we recover the ordinary N=2 superconformal
algebra.
We also give a Heisenberg representation of the algebra, making a twist
of the $U(1)$ boson in the Wakimoto representation of the quantum
affine algebra $U_q(\widehat{sl}_2)$.
(Based on a collaboration with H. Awata, K. Harada and H. Kanno.)
Time: 4:00 pm, Wednesday, 27th November, 2024
Location: Room 1610 at SIMIS, Block A, No. 657 Songhu Road, Yangpu District, Shanghai
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