A qq-multinomial expansion of LLT coefficients and plethysm multiplicities

Lascoux, Leclerc and Thibon (1997) [9] introduced a family of symmetric polynomials, called LLT polynomials. We prove a qq-multinomial expansion of the coefficients of LLT polynomials in the case where μ=(μ,⋯,μ)︸n and define a qq-analog of a sum of the plethysm multiplicities.