The Index and Spectrum of Lie Poset Algebras of Types B, C, and D

We define posets of types B, C, and D. These encode the matrix forms certain Lie algebras which lie between upper-triangular diagonal matrices. Our primary concern is index spectral theories such type-B, D poset algebras. For an important restricted class, we develop combinatorial formulas and, in particular, characterize corresponding to Frobenius In this latter case show that spectrum binary; is, consists equal number 0's 1's. Interestingly, can be related Reiner's notion a parset.