Extended Schur functions and bases related by involutions

We introduce two new bases of QSym, , the reverse extended Schur functions and the row-strict reverse extended Schur functions, as well as their duals in NSym, , the reverse shin functions and row-strict reverse shin functions. These bases are the images of the extended Schur basis and shin basis under the involutions rho and w , which generalize the classical involution w on the symmetric functions. In addition, we prove a Jacobi-Trudi rule for certain shin functions using creation operators. We define skew extended Schur functions and skew- II extended Schur functions based on left and right actions of NSym and QSym respectively. We then use the involutions rho and w to translate these and other known results to our reverse and row-strict reverse bases. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.