Noncommutative Schur polynomials and the crystal limit of the U_q sl(2)-vertex model

Starting from the Verma module of U_q sl(2) we consider the evaluation module for affine U_q sl(2) and discuss its crystal limit (q=0). There exists an associated integrable statistical mechanics model on a square lattice defined in terms of vertex configurations. Its transfer matrix is the generating function for noncommutative complete symmetric polynomials in the generators of the affine plactic algebra, an extension of the finite plactic algebra first discussed by Lascoux and Sch\"{u}tzenberger. The corresponding noncommutative elementary symmetric polynomials were recently shown to be generated by the transfer matrix of the so-called phase model discussed by Bogoliubov, Izergin and Kitanine. Here we establish that both generating functions satisfy Baxter's TQ-equation in the crystal limit by tying them to special U_q sl(2) solutions of the Yang-Baxter equation. The TQ-equation amounts to the well-known Jacobi-Trudy formula leading naturally to the definition of noncommutative Schur polynomials. The latter can be employed to define a ring which has applications in conformal field theory and enumerative geometry: it is isomorphic to the fusion ring of the sl(n)_k -WZNW model whose structure constants are the dimensions of spaces of generalized theta-functions over the Riemann sphere with three punctures.Comment: 24 pages, 6 figures; v2: several typos fixe

A (p,q) Deformation of the Universal Enveloping Superalgebra U(osp(2/2))

We investigate a two parameter quantum deformation of the universal enveloping orthosymplectic superalgebra U(osp(2/2)) by extending the Faddeev-Reshetikhin-Takhtajan formalism to the supersymetric case. It is shown that $U_{p,q}(osp(2/2))$ possesses a non-commutative, non-cocommutative Hopf algebra structure. All the results are expressed in the standard form using quantum Chevalley basis.Comment: 8 pages; IC/93/41

Difference L operators related to q-characters

We introduce a factorized difference operator L(u) annihilated by the Frenkel-Reshetikhin screening operator for the quantum affine algebra U_q(C^{(1)}_n). We identify the coefficients of L(u) with the fundamental q-characters, and establish a number of formulas for their higher analogues. They include Jacobi-Trudi and Weyl type formulas, canceling tableau sums, Casorati determinant solution to the T-system, and so forth. Analogous operators for the orthogonal series U_q(B^{(1)}_n) and U_q(D^{(1)}_n) are also presented.Comment: 25 pages, LaTeX2e, no figur

Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case

In proving the Fermionic formulae, combinatorial bijection called the Kerov--Kirillov--Reshetikhin (KKR) bijection plays the central role. It is a bijection between the set of highest paths and the set of rigged configurations. In this paper, we give a proof of crystal theoretic reformulation of the KKR bijection. It is the main claim of Part I (math.QA/0601630) written by A. Kuniba, M. Okado, T. Takagi, Y. Yamada, and the author. The proof is given by introducing a structure of affine combinatorial $R$ matrices on rigged configurations.Comment: 45 pages, version for publication. Introduction revised, more explanations added to the main tex

Integrable multiparametric quantum spin chains

Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted boundary conditions. We illustrate how this general formalism applies to construct multiparametric versions of the supersymmetric t-J and U models.Comment: 17 pages, RevTe

Tetrahedron and 3D reflection equations from quantized algebra of functions

Soibelman's theory of quantized function algebra A_q(SL_n) provides a representation theoretical scheme to construct a solution of the Zamolodchikov tetrahedron equation. We extend this idea originally due to Kapranov and Voevodsky to A_q(Sp_{2n}) and obtain the intertwiner K corresponding to the quartic Coxeter relation. Together with the previously known 3-dimensional (3D) R matrix, the K yields the first ever solution to the 3D analogue of the reflection equation proposed by Isaev and Kulish. It is shown that matrix elements of R and K are polynomials in q and that there are combinatorial and birational counterparts for R and K. The combinatorial ones arise either at q=0 or by tropicalization of the birational ones. A conjectural description for the type B and F_4 cases is also given.Comment: 26 pages. Minor correction

Character Formulae of sl^n\hat{sl}_n-Modules and Inhomogeneous Paths

Let B_{(l)} be the perfect crystal for the l-symmetric tensor representation of the quantum affine algebra U'_q(\hat{sl(n)}). For a partition mu = (mu_1,...,mu_m), elements of the tensor product B_{(mu_1)} \otimes ... \otimes B_{(mu_m)} can be regarded as inhomogeneous paths. We establish a bijection between a certain large mu limit of this crystal and the crystal of an (generally reducible) integrable U_q(\hat{sl(n)})-module, which forms a large family depending on the inhomogeneity of mu kept in the limit. For the associated one dimensional sums, relations with the Kostka-Foulkes polynomials are clarified, and new fermionic formulae are presented. By combining their limits with the bijection, we prove or conjecture several formulae for the string functions, branching functions, coset branching functions and spinon character formula of both vertex and RSOS types.Comment: 42 pages, LaTeX2.0

Neural Correlates of True Memory, False Memory, and Deception

We used functional magnetic resonance imaging (fMRI) to determine whether neural activity can differentiate between true memory, false memory, and deception. Subjects heard a series of semantically related words and were later asked to make a recognition judgment of old words, semantically related nonstudied words (lures for false recognition), and unrelated new words. They were also asked to make a deceptive response to half of the old and unrelated new words. There were 3 main findings. First, consistent with the notion that executive function supports deception, 2 types of deception (pretending to know and pretending not to know) recruited prefrontal activity. Second, consistent with the sensory reactivation hypothesis, the difference between true recognition and false recognition was found in the left temporoparietal regions probably engaged in the encoding of auditorily presented words. Third, the left prefrontal cortex was activated during pretending to know relative to correct rejection and false recognition, whereas the right anterior hippocampus was activated during false recognition relative to correct rejection and pretending to know. These findings indicate that fMRI can detect the difference in brain activity between deception and false memory despite the fact that subjects respond with “I know” to novel events in both processes

The development of descending projections from the brainstem to the spinal cord in the fetal sheep

<p>Abstract</p> <p>Background</p> <p>Although the fetal sheep is a favoured model for studying the ontogeny of physiological control systems, there are no descriptions of the timing of arrival of the projections of supraspinal origin that regulate somatic and visceral function. In the early development of birds and mammals, spontaneous motor activity is generated within spinal circuits, but as development proceeds, a distinct change occurs in spontaneous motor patterns that is dependent on the presence of intact, descending inputs to the spinal cord. In the fetal sheep, this change occurs at approximately 65 days gestation (G65), so we therefore hypothesised that spinally-projecting axons from the neurons responsible for transforming fetal behaviour must arrive at the spinal cord level shortly before G65. Accordingly we aimed to identify the brainstem neurons that send projections to the spinal cord in the mature sheep fetus at G140 (term = G147) with retrograde tracing, and thus to establish whether any projections from the brainstem were absent from the spinal cord at G55, an age prior to the marked change in fetal motor activity has occurred.</p> <p>Results</p> <p>At G140, CTB labelled cells were found within and around nuclei in the reticular formation of the medulla and pons, within the vestibular nucleus, raphe complex, red nucleus, and the nucleus of the solitary tract. This pattern of labelling is similar to that previously reported in other species. The distribution of CTB labelled neurons in the G55 fetus was similar to that of the G140 fetus.</p> <p>Conclusion</p> <p>The brainstem nuclei that contain neurons which project axons to the spinal cord in the fetal sheep are the same as in other mammalian species. All projections present in the mature fetus at G140 have already arrived at the spinal cord by approximately one third of the way through gestation. The demonstration that the neurons responsible for transforming fetal behaviour in early ontogeny have already reached the spinal cord by G55, an age well before the change in motor behaviour occurs, suggests that the projections do not become fully functional until well after their arrival at the spinal cord.</p

Visual imagery and false memory for pictures:a functional magnetic resonance imaging study in healthy participants

BACKGROUND: Visual mental imagery might be critical in the ability to discriminate imagined from perceived pictures. Our aim was to investigate the neural bases of this specific type of reality-monitoring process in individuals with high visual imagery abilities. METHODS: A reality-monitoring task was administered to twenty-six healthy participants using functional magnetic resonance imaging. During the encoding phase, 45 words designating common items, and 45 pictures of other common items, were presented in random order. During the recall phase, participants were required to remember whether a picture of the item had been presented, or only a word. Two subgroups of participants with a propensity for high vs. low visual imagery were contrasted. RESULTS: Activation of the amygdala, left inferior occipital gyrus, insula, and precuneus were observed when high visual imagers encoded words later remembered as pictures. At the recall phase, these same participants activated the middle frontal gyrus and inferior and superior parietal lobes when erroneously remembering pictures. CONCLUSIONS: The formation of visual mental images might activate visual brain areas as well as structures involved in emotional processing. High visual imagers demonstrate increased activation of a fronto-parietal source-monitoring network that enables distinction between imagined and perceived pictures