71.9 Inducing and restricting modules

Specht provides four functions InducedModule, RestrictedModule, SInducedModule and SRestrictedModule for inducing and restricting modules. All functions can be applied to Specht modules, PIMs, and simple modules. These functions all work by first rewriting all modules as a linear combination of Specht modules (or q--Weyl modules), and then inducing and restricting. Whenever possible the induced or restricted module will be written in the original basis.

All of these functions can also be applied to elements of the Fock space (see Specht); in which case they correspond to the action of the generators E_i and F_i of U_q(widehat{sl_e}) on F. There is also a function InducedDecompositionMatrix InducedDecompositionMatrix for inducing decomposition matrices.

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