Factorial skew Schur functions and Schur Q-functions (I)

      Schur symmetric functions and their skew versions have a variety of determinantal expansions including the Jacobi-Trudi identity, its dual identity and the Giambelli identity. These are all special cases of determinantal identities based on outside decompositions of Young diagrams due to Hamel and Goulden. Chen, Yan and Yang introduced the key notion of cutting strips to generate outside decompositions. It will be shown that cutting strips enable one to derive not only these identities but also those applicable to factorial skew Schur functions by exploiting non-intersecting path models of Young tableaux. If time allows the same techniques will be shown to apply to skew Schur Q-functions and their factorial versions leading to a family of expansions in terms of Pfaffians. Copious use will be made of illustrative examples.