A quantum deformation of the N=2 superconformal algebra

We introduce a unital associative algebra SVir\!q,k, having q and k as complex parameters, generated by the elements K^±ₘ (± m≥ 0), Tₘ (m∈ Z), and G^±ₘ (m∈ Z+1 2 in the Neveu-Schwarz sector, m∈ Z in the Ramond sector), satisfying relations which are at most quartic. Calculations of some low-lying Kac determinants are made, providing us with a conjecture for the factorization property of the Kac determinants. The analysis of the screening operators gives a supporting evidence for our conjecture. It is shown that by taking the limit q→ 1 of SVir\!q,k we recover the ordinary N=2 superconformal algebra. We also give a nontrivial Heisenberg representation of the algebra SVir\!q,k, making a twist of the $U(1)$ boson in the Wakimoto representation of the quantum affine algebra Uq(sl₂), which naturally follows from the construction of SVir\!q,k by gluing the deformed Y-algebras of Gaiotto and Rapc\'{a}k.