Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters

We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form. We exploit the fact that quantum non-compact algebras such as $U_q(su(1,1))$ and type-I quantum superalgebras such as $U_q(gl(1|1))$ and $U_q(gl(2|1))$ are known to admit non-trivial one-parameter families of infinite-dimensional and finite dimensional irreps, respectively, even for generic $q$. We develop a technique for constructing the corresponding spectral-dependent R-matrices. As examples we work out the the $R$-matrices for the three quantum algebras mentioned above in certain representations.Comment: 13 page

Infinite Families of Gauge-Equivalent RR-Matrices and Gradations of Quantized Affine Algebras

Associated with the fundamental representation of a quantum algebra such as $U_q(A_1)$ or $U_q(A_2)$, there exist infinitely many gauge-equivalent $R$-matrices with different spectral-parameter dependences. It is shown how these can be obtained by examining the infinitely many possible gradations of the corresponding quantum affine algebras, such as $U_q(A_1^{(1)})$ and $U_q(A_2^{(1)})$, and explicit formulae are obtained for those two cases. Spectral-dependent similarity (gauge) transformations relate the $R$-matrices in different gradations. Nevertheless, the choice of gradation can be physically significant, as is illustrated in the case of quantum affine Toda field theories.Comment: 14 pages, Latex, UQMATH-93-10 (final version for publication

The structure of quantum Lie algebras for the classical series B_l, C_l and D_l

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at $q=1$. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint x adjoint ---> adjoint. We present a practical method for the determination of these quantum Clebsch-Gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum Lie algebras associated to the classical Lie algebras B_l, C_l and D_l. In the quantum case also the structure constants of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invariant Killing form on the quantum Lie algebras and find that it takes values which are simple q-deformations of the classical ones.Comment: 25 pages, amslatex, eepic. Final version for publication in J. Phys. A. Minor misprints in eqs. 5.11 and 5.12 correcte

Scanning Electron Microscopy of the Lateral Ventricle of the Pigeon Brain

Adult pigeons of both sexes were used for this study. Depending upon the distribution of various surface profiles, for example cilia, microvilli and blebs, ependymal areas with differing surface patterns were distinguished in the lateral ventricle. The topographical locations of these areas with respect to the underlying forebrain nuclei were determined in accord with the atlas of Karten and Hodos (1967). The medial surface (A) of the ventricle was much more densely ciliated than the lateral surface (B). There did not appear to be any correlation between a given surface pattern and a specific type of underlying nervous tissue. Comparison of the cell patterns seen in the pigeon brain with those seen in the analogous areas of the rat brain showed that it is not feasible to extrapolate from one zoological group to another. With the exception of the Kolmer cells populating the choroid plexus, there were remarkably few supraependymal cells in the pigeon lateral ventricle. Supraependymal nerve fibers were also extremely rare. Particular attention was given to the ependyma associated with the nucleus stria terminalis, to that of the lateral septal organ and to the choroid plexus. The possible classification of these areas into the group of the circumventricular organs is considered

Quantum affine Toda solitons

We review some of the progress in affine Toda field theories in recent years, explain why known dualities cannot easily be extended, and make some suggestions for what should be sought instead.Comment: 16pp, LaTeX. Minor revision