Colored fermionic vertex models and symmetric functions

In this text we introduce and analyze families of symmetric functions arising as partition for colored fermionic vertex models associated with the quantized affine Lie superalgebra $U_q \big ( \widehat {\mathfrak {sl}} (1 | n) )$. We establish various combinatorial results these functions, which include following. apply fusion procedure to fundamental $R$-matrix )$ obtain an explicit family weights satisfying Yang–Baxter equation. define colored, under fused weights. further several properties such branching rules Cauchy identities. show that Lascoux–Leclerc–Thibon (LLT) polynomials arise special cases functions. This enables us both old new about LLT polynomials, including identities, contour integral formulas, stability properties, a certain plethystic transformations. A different case our gives rise called factorial polynomials. they generalize while also vanishing condition reminiscent satisfied by Schur By considering model on cylinder, function formulas nonsymmetric Macdonald prove coefficients when expanded in modified Hall–Littlewood basis, (2 model.