Abstract. In this paper, we give an explicit combinatorial realization of the crystal B(λ) for an irreducible highest weight U q (q(n))-module V (λ) in terms of semistandard decomposition tableaux. We present an insertion scheme for semistandard decomposition tableaux and give algorithms of decomposing the tensor product of q(n)-crystals. Consequently, we obtain explicit combinatorial descriptions of the shifted LittlewoodRichardson coefficients.

In the present study, we assessed efficacy of exosomes harvested from human and mouse stem cell cultures in protection of mouse primary astrocyte and neuronal cell cultures following in vitro ischemia, and against ischemic stroke in vivo. Cell media was collected from primary mouse neural stem cell (NSC) cultures or from human induced pluripotent stem cell-derived cardiomyocyte (iCM) cultures. Exosomes were extracted and purified by polyethylene glycol complexing and centrifugation, and exosome size and concentration were determined with a NanoSiteTM particle analyzer. Exosomes were applied to primary mouse cortical astrocyte or neuronal cultures prior to, and/or during, combined oxygen-glucose deprivation (OGD) injury. Cell death was assessed via lactate dehydrogenase (LHD) and propidium iodide staining 24 h after injury. NSC-derived exosomes afforded marked protection to astrocytes following OGD. A more modest (but significant) level of protection was observed with human iCM-derived exosomes applied to astrocytes, and with NSC-derived exosomes applied to primary neuronal cultures. In subsequent experiments, NSC-derived exosomes were injected intravenously into adult male mice 2 h after transient (1 h) middle cerebral artery occlusion (MCAO). Gross motor function was assessed 1 day after reperfusion and infarct volume was assessed 4 days after reperfusion. Mice treated post-stroke with intravenous NSC-derived exosomes exhibited significantly reduced infarct volumes. Together, these results suggest that exosomes isolated from mouse NSCs provide neuroprotection against experimental stroke possibly via preservation of astrocyte function. Intravenous NSC-derived exosome treatment may therefore provide a novel clinical adjuvant for stroke in the immediate post-injury period.

Abstract. In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra Uq(q(n)). The key ingredients are the triangular decomposition of Uq(q(n)) and the classification of finite dimensional irreducible modules over quantum Clifford superalgebras. The main results we prove are the classical limit theorem and the complete reducibility theorem for Uq(q(n))-modules in the category O ≥0 q .

Abstract. In this paper, we develop the crystal basis theory for the quantum queer superalgebra U q (q(n)). We define the notion of crystal bases and prove the tensor product rule for U q (q(n))-modules in the category O ≥0int . Our main theorem shows that every U q (q(n))-module in the category O ≥0 int has a unique crystal basis.