LP = bgg P
RM = bgg(M,LengthLimit=>4)
If P is an E-module, then LP becomes a linear complex of free S-modules, where (S,E) is the Koszul pair corresponding to a product of projective spaces. Similarly, if M is an S-module, them RM becomes a linear free complex over the exterior algebra E of length bounded by the LengthLimit.
The complex LP is that produced from P by the Bernstein-Gel'fand-Gel'fand functor called L in our paper Tate Resolutions on Products of Projective Spaces. Similarly, the complex RM produced from M is a bounded piece of the infinite complex of the Bernstein-Gel'fand-Gel'fand functor called R in loc.cit. L and R form a pair of adjoint functors.
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The object bgg is a method function with options.