Generators of supersymmetric polynomials in positive characteristic

In Kantor and Trishin (1997) [3], Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl(m vertical bar n) and a related algebra A, of what they called pseudosymmetric polynomials over an algebraically closed field K of characteristic zero. The algebra A(s) was investigated earlier by Stembridge (1985) who in [9] called the elements of A(s) supersymmetric polynomials and determined generators of A(s). The case of positive characteristic p of the ground field K has been recently investigated by La Scala and Zubkov (in press) in [6]. We extend their work and give a complete description of generators of polynomial invariants of the adjoint action of the general linear supergroup GL(m vertical bar n) and generators of A(s).

Purinergic and glutamatergic interactions in the hypothalamic paraventricular nucleus modulate sympathetic outflow

P2X receptors are expressed on ventrolateral medulla projecting paraventricular nucleus (PVN) neurons. Here, we investigate the role of adenosine 5′-triphosphate (ATP) in modulating sympathetic nerve activity (SNA) at the level of the PVN. We used an in situ arterially perfused rat preparation to determine the effect of P2 receptor activation and the putative interaction between purinergic and glutamatergic neurotransmitter systems within the PVN on lumbar SNA (LSNA). Unilateral microinjection of ATP into the PVN induced a dose-related increase in the LSNA (1 nmol: 38 ± 6 %, 2.5 nmol: 72 ± 7 %, 5 nmol: 96 ± 13 %). This increase was significantly attenuated by blockade of P2 receptors (pyridoxalphosphate-6-azophenyl-20,40-disulphonic acid, PPADS) and glutamate receptors (kynurenic acid, KYN) or a combination of both. The increase in LSNA elicited by L-glutamate microinjection into the PVN was not affected by a previous injection of PPADS. Selective blockade of non-N-methyl-D-aspartate receptors (6-cyano-7-nitroquinoxaline-2,3-dione disodium salt, CNQX), but not N-methyl-D-aspartate receptors (NMDA) receptors (DL-2-amino-5-phosphonopentanoic acid, AP5), attenuated the ATP-induced sympathoexcitatory effects at the PVN level. Taken together, our data show that purinergic neurotransmission within the PVN is involved in the control of SNA via P2 receptor activation. Moreover, we show an interaction between P2 receptors and non-NMDA glutamate receptors in the PVN suggesting that these functional interactions might be important in the regulation of sympathetic outflow