root system

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root system

the total below-ground vegetative system of vascular plants. see ROOT.

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Given a positive root [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], there is an associated root vector [x.sub.[beta]] [member of] [B.sub.q] defined via the so-called Lusztig isomorphisms [H3].

A finite-dimensional Lie algebra arising from a Nichols algebra of diagonal type (rank 2)

The system of root vectors of a compact dissipative operator B with nuclear imaginary component is complete in the Hilbert space H so long as at least one of the following two conditions is fulfilled:

On q-Sturm Liouville operators with eigenvalue parameter contained in the boundary conditions

Notice that the kth element of the root vector of B, km - [b.sub.k], is the number of cells in the kth column of [[DELTA].sub.N,m] which lie outside of board B.