Browsing by Author "King, Ronald C."
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- ItemPlethysms, replicated Schur functions, and series, with applications to vertex operators(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2010) Fauser, Bertfried; Jarvis, Peter D.; King, Ronald C.Specializations of Schur functions are exploited to define and evaluate the Schur functions sλ[αX] and plethysms sλ[αsν(X))] for any α-integer, real or complex. Plethysms are then used to define pairs of mutually inverse infinite series of Schur functions, Mπ and Lπ, specified by arbitrary partitions π. These are used in turn to define and provide generating functions for formal characters, s(π)λ, of certain groups Hπ, thereby extending known results for orthogonal and symplectic group characters. Each of these formal characters is then given a vertex operator realization, first in terms of the series M=M(0) and various L⊥σ dual to Lσ, and then more explicitly in exponential form. Finally the replicated form of such vertex operators are written down.
- ItemPlethystic vertex operators and boson-fermion correspondences(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Fauser, Bertfried; Jarvis, Peter D.; King, Ronald C.We study the algebraic properties of plethystic vertex operators, introduced in J. Phys. A: Math. Theor. 43 405202 (2010), underlying the structure of symmetric functions associated with certain generalized universal character rings of subgroups of the general linear group, defined to stabilize tensors of Young symmetry type characterized by a partition of arbitrary shape π. Here we establish an extension of the well-known boson-fermion correspondence involving Schur functions and their associated (Bernstein) vertex operators: for each π, the modes generated by the plethystic vertex operators and their suitably constructed duals, satisfy the anticommutation relations of a complex Clifford algebra. The combinatorial manipulations underlying the results involve exchange identities exploiting the Hopfalgebraic structure of certain symmetric function series and their plethysms.