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FFLV-type monomial bases for type $$B$$. (English) Zbl 07049527
Summary: We present a combinatorial monomial basis (or, more precisely, a family of monomial bases) in every finite-dimensional irreducible $$\mathfrak{so}_{2n+1}$$-module. These bases are in many ways similar to the FFLV bases for types $$A$$ and $$C$$. They are also defined combinatorially via sums over Dyck paths in certain triangular grids. Our sums, however, involve weights depending on the length of the corresponding root. Accordingly, our bases also induce bases in certain degenerations of the modules but these degenerations are obtained not from the filtration by PBW degree but by a weighted version thereof.

##### MSC:
 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17B20 Simple, semisimple, reductive (super)algebras 05E10 Combinatorial aspects of representation theory
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