Solution of 2D Ising model on triangular lattice by auxiliary $q$-deformed Grassmann field method

The representation of the partition function of the inhomogeneous 2D Ising model on triangular lattice (coupling parameters are arbitrary functions of coordinates) is derived in terms of the functional Grassmann integral. To transform the partition function into the integral we use an auxiliary six-component Grassmann field. Grassmann variables corresponding to the one of the components commute with others. Thus, one pair of components realizes the representation of the $q$-deformed group $SL_q(2,R)$ with ($q=-1$). The other two pairs are the usual Grassmann spinors ($q=1$). An explicit expression for the Gaussian integral over such fields is obtained through the modified Pfaffian. A connection with the usual Grassmann functional integral is also obtained.