In this talk, we give the construction of the equivariant Hodge realization of the polylogarithm class for the algebraic torus associated to totally real fields. We will then give its relation to the Shintani generating class, a class in equivariant coherent cohomology which generates the special values of Lerch zeta functions. We will then state a conjecture concerning the plectic version of this construction and its implication to the Beilinson conjecture in this case. This is a joint work with Hohto Bekki, Kei Hagihara, Tetsuya Ohshita, Kazuki Yamada, and Shuji Yamamoto.