104 research outputs found
Quantum groups and Cabibbo mixing
Treating the issue of hadron masses and mass relations by the use of quantum
groups U_q(su_n) taken as hadron flavor symmetries suggests, at least in the
case of baryons, a direct connection of the deformation parameter q with the
Cabibbo angle. We discuss possible manifestations of the Cabibbo mixing implied
by such connection, including unusual ones.Comment: 8 pages, 1 figure, LaTeX; talk given at the 5th International
Conference "Symmetry in Nonlinear Mathematical Physics", Kyiv (Kiev),
Ukraine, June 23-29, 200
On Chebyshev polynomials and torus knots
In this work we demonstrate that the q-numbers and their two-parameter
generalization, the q,p-numbers, can be used to obtain some polynomial
invariants for torus knots and links. First, we show that the q-numbers, which
are closely connected with the Chebyshev polynomials, can also be related with
the Alexander polynomials for the class T(s,2) of torus knots, s being an odd
integer, and used for finding the corresponding skein relation. Then, we
develop this procedure in order to obtain, with the help of q,p-numbers, the
generalized two-variable Alexander polynomials, and prove their direct
connection with the HOMFLY polynomials and the skein relation of the latter.Comment: 6 pages (two-column UJP style
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