10,768 research outputs found

    Backlund transformations for the sl(2) Gaudin magnet

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    Elementary, one- and two-point, Backlund transformations are constructed for the generic case of the sl(2) Gaudin magnet. The spectrality property is used to construct these explicitly given, Poisson integrable maps which are time-discretizations of the continuous flows with any Hamiltonian from the spectral curve of the 2x2 Lax matrix

    <i>esp1-1</i> functional interaction map derived from the SL SGA screen.

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    <p>The 161 genes identified in the <i>esp1-1</i> SL screen were analyzed using Cytoscape. All nodes represent significantly enriched (p <0.05) GO Terms in the dataset. Coloured nodes represent GO Terms that have been grouped into a category (written in the same colour) that is significantly enriched. Edges define associations between groups and edge thickness indicates the level of significance within the network. Genes identified in the SL screen that are associated with GO Terms are shown.</p

    2-d Gravity as a limit of the SL(2,R) Black Hole

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    The transformation of the SL(2; R)=U(1) black hole under a boost of the subgroup U(1) is studied. It is found that the tachyon vertex operators of the black hole go into those of the c = 1 conformal field theory coupled to gravity. The discrete states of the black hole also tend to the discrete states of the 2-d gravity theory. The fate of the extra discrete states of the black hole under boost are discussed. 1 Introduction The relation between the two simple string theory models in two dimensions, the critical U(1) gauged WZW SL(2; R) model [1\Gamma4] , and the noncritical string theory of a one dimensional matter field coupled to Liouville field, has attracted considerable attention [5\Gamma14] . In Ref.[1] it was argued that as it is not possible to remove one of the parameters of the two dimensional black hole in favour of the Liouville field in all the regions of the black hole geometry, the theory can not be regarded as a non-critical string theory of c = 1 matter couple..

    CR1 Knops blood group alleles are not associated with severe malaria in the Gambia

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    The Knops blood group antigen erythrocyte polymorphisms have been associated with reduced falciparum malaria-based in vitro rosette formation (putative malaria virulence factor). Having previously identified single-nucleotide polymorphisms (SNPs) in the human complement receptor 1 (CR1/CD35) gene underlying the Knops antithetical antigens Sl1/Sl2 and McC(a)/McC(b), we have now performed genotype comparisons to test associations between these two molecular variants and severe malaria in West African children living in the Gambia. While SNPs associated with Sl:2 and McC(b+) were equally distributed among malaria-infected children with severe malaria and control children not infected with malaria parasites, high allele frequencies for Sl 2 (0.800, 1,365/1,706) and McC(b) (0.385, 658/1706) were observed. Further, when compared to the Sl 1/McC(a) allele observed in all populations, the African Sl 2/McC(b) allele appears to have evolved as a result of positive selection (modified Nei-Gojobori test Ka-Ks/s.e.=1.77, P-valu

    Branching Law for the Finite Subgroups of SL(4,C)

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    9 pagesIn the framework of McKay correspondence we determine, for every finite subgroup Γ\Gamma of SL4C\mathbf{SL}_4\mathbb{C}, how the finite dimensional irreducible representations of SL4C\mathbf{SL}_4\mathbb{C} decompose under the action of Γ\Gamma.\\ Let \go{h} be a Cartan subalgebra of \go{sl}_4\mathbb{C} and let ϖ1,ϖ2,ϖ3\varpi_1,\,\varpi_2,\,\varpi_3 be the corresponding fundamental weights. For (p,q,r)N3(p,q,r)\in \mathbb{N}^3, the restriction πp,q,rΓ\pi_{p,q,r}|_\Gamma of the irreducible representation πp,q,r\pi_{p,q,r} of highest weight pϖ1+qϖ2+rϖ3p\varpi_1+q\varpi_2+r\varpi_3 of SL4C\mathbf{SL}_4\mathbb{C} decomposes as πp,q,rΓ=i=0lmi(p,q,r)γi.{\pi_{p,q,r}}|_{\Gamma}=\bigoplus_{i=0}^l m_i(p,q,r)\gamma_i. We determine the multiplicities mi(p,q,r)m_i(p,q,r) and prove that the series PΓ(t,u,w)i=p=0q=0r=0mi(p,q,r)tpuqwrP_\Gamma(t,u,w)_i=\sum_{p=0}^\infty\sum_{q=0}^\infty\sum_{r=0}^\infty m_i(p,q,r)t^pu^qw^r are rational functions.\\ This generalizes results from Kostant for SL2C\mathbf{SL}_2\mathbb{C} and our preceding works about SL3C\mathbf{SL}_3\mathbb{C}

    Branching Law for the Finite Subgroups of SL(4,C)

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    9 pagesIn the framework of McKay correspondence we determine, for every finite subgroup Γ\Gamma of SL4C\mathbf{SL}_4\mathbb{C}, how the finite dimensional irreducible representations of SL4C\mathbf{SL}_4\mathbb{C} decompose under the action of Γ\Gamma.\\ Let \go{h} be a Cartan subalgebra of \go{sl}_4\mathbb{C} and let ϖ1,ϖ2,ϖ3\varpi_1,\,\varpi_2,\,\varpi_3 be the corresponding fundamental weights. For (p,q,r)N3(p,q,r)\in \mathbb{N}^3, the restriction πp,q,rΓ\pi_{p,q,r}|_\Gamma of the irreducible representation πp,q,r\pi_{p,q,r} of highest weight pϖ1+qϖ2+rϖ3p\varpi_1+q\varpi_2+r\varpi_3 of SL4C\mathbf{SL}_4\mathbb{C} decomposes as πp,q,rΓ=i=0lmi(p,q,r)γi.{\pi_{p,q,r}}|_{\Gamma}=\bigoplus_{i=0}^l m_i(p,q,r)\gamma_i. We determine the multiplicities mi(p,q,r)m_i(p,q,r) and prove that the series PΓ(t,u,w)i=p=0q=0r=0mi(p,q,r)tpuqwrP_\Gamma(t,u,w)_i=\sum_{p=0}^\infty\sum_{q=0}^\infty\sum_{r=0}^\infty m_i(p,q,r)t^pu^qw^r are rational functions.\\ This generalizes results from Kostant for SL2C\mathbf{SL}_2\mathbb{C} and our preceding works about SL3C\mathbf{SL}_3\mathbb{C}

    Branching Law for the Finite Subgroups of SL(4,C)

    No full text
    9 pagesIn the framework of McKay correspondence we determine, for every finite subgroup Γ\Gamma of SL4C\mathbf{SL}_4\mathbb{C}, how the finite dimensional irreducible representations of SL4C\mathbf{SL}_4\mathbb{C} decompose under the action of Γ\Gamma.\\ Let \go{h} be a Cartan subalgebra of \go{sl}_4\mathbb{C} and let ϖ1,ϖ2,ϖ3\varpi_1,\,\varpi_2,\,\varpi_3 be the corresponding fundamental weights. For (p,q,r)N3(p,q,r)\in \mathbb{N}^3, the restriction πp,q,rΓ\pi_{p,q,r}|_\Gamma of the irreducible representation πp,q,r\pi_{p,q,r} of highest weight pϖ1+qϖ2+rϖ3p\varpi_1+q\varpi_2+r\varpi_3 of SL4C\mathbf{SL}_4\mathbb{C} decomposes as πp,q,rΓ=i=0lmi(p,q,r)γi.{\pi_{p,q,r}}|_{\Gamma}=\bigoplus_{i=0}^l m_i(p,q,r)\gamma_i. We determine the multiplicities mi(p,q,r)m_i(p,q,r) and prove that the series PΓ(t,u,w)i=p=0q=0r=0mi(p,q,r)tpuqwrP_\Gamma(t,u,w)_i=\sum_{p=0}^\infty\sum_{q=0}^\infty\sum_{r=0}^\infty m_i(p,q,r)t^pu^qw^r are rational functions.\\ This generalizes results from Kostant for SL2C\mathbf{SL}_2\mathbb{C} and our preceding works about SL3C\mathbf{SL}_3\mathbb{C}
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