Hidden TEX

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Headers

Pensieve header: The PBW multiplication tensor for  $gl_{n,\epsilon}$ using the nilpotent-only $\lambda$-tangent formalism. Some material from pensive://Projects/glneps and from pensieve://Projects/UEA.

SetDirectory@"C:\\drorbn\\AcademicPensieve\\Projects\\SolvablePBW";
<< KnotTheory`

nb2tex

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Conventions on August 18

Only one algebra (not necessarily Lie!) at a time, and it comes with a list of (Latin) generators and their Greek duals, and a default PBW order. If some Verma module is needed, it is added once and by means of extra generators.
Generators are of the form (Subscript[x, α,β])[i], (Subscript[a, α])[i], etc., where i is the tensor factor.
In the commutative context we have (Subscript[𝔼, i,j->k])[(Subscript[L, 0]),(Subscript[L, 1]),...], where (Subscript[L, p]) is the coefficient of (ϵ^p), and (maybe) (Subscript[𝕆, i,j->k])[F].
In the non-commutative context, generators do not carry a “tensor factor” designations. Instead we consider expressions like (Subscript[U, i])[x,y,y,x].

Issues: Upper and lower?