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We prove orthogonality and compute explicitly the (quadratic) norms for super‐Jack polynomials    S   P  λ    (   (   z  1   ,  …  ,   z  n   )   ,   (   w  1   ,  …  ,   w  m   )   ;  θ  )with respect to a natural positive semi‐definite, but degenerate, Hermitian product⟨  ·  ,  ·  ⟩    n  ,  m  ,  θ   ′   . In case    m  =  0    (or    n  =  0   ), our product reduces to Macdonald's well‐known inner product⟨  ·  ,  ·  ⟩    n  ,  θ   ′   , and we recover his corresponding orthogonality results for the Jack polynomialsP  λ    (   (   z  1   ,  …  ,   z  n   )   ;  θ  )    . From our main results, we readily infer that the kernel of⟨  ·  ,  ·  ⟩    n  ,  m  ,  θ   ′    is spanned by the super‐Jack polynomials indexed by a partition   λ   not containing the    m  ×  n    rectangle    (   m  n   )   . As an application, we provide a Hilbert space interpretation of the deformed trigonometric Calogero–Moser–Sutherland operators of type    A  (  n  −  1  ,  m  −  1  )   .

Orthogonality of super‐Jack polynomials and a Hilbert space interpretation of deformed Calogero–Moser–Sutherland operators