Generating functions for the universal Hall-Littlewood PP- and QQ-functions

Recently, P. Pragacz described the ordinary Hall-Littlewood $P$-polynomials by means of push-forwards (Gysin maps) from flag bundles in the ordinary cohomology theory. Together with L. Darondeau, he also gave push-forward formulas (Gysin formulas) for all flag bundles of types $A$, $B$, $C$ and $D$ in the ordinary cohomology theory. In this paper, we introduce a generalization of the ordinary Hall-Littlewood $P$- and $Q$-polynomials, which we call the {\it universal $($factorial$)$ Hall-Littlewood $P$- and $Q$-functions}, and characterize them in terms of Gysin maps from flag bundles in the complex cobordism theory. We also generalize the (type $A$) push-forward formula due to Darondeau-Pragacz to the complex cobordism theory. As an application of our Gysin formulas in complex cobordism, we give generating functions for the universal Hall-Littlewood $P$- and $Q$-functions and their factorial analogues. Using our generating functions, classical determinantal and Pfaffian formulas for Schur $S$- and $Q$-polynomials, and their $K$-theoretic or factorial analogues can be obtained in a simple and unified manner.Comment: 46 pages, AMSLaTeX; Section 6 added, An error of the generating function for the universal factorial Hall-Littlewood $P$-functions was correcte

Aspects of the phonetic and phonological structure of the G/ui language

ABSTRACT This study describes selected aspects of the phonetic and phonological structure of the G|ui language, a poorly documented endangered Khoe (Central Khoisan) language spoken in Botwana. It conducts instrumental phonetic investigations, namely analyses of palatograms, linguograms, aerodynamic recordings, sound spectrograms, spectra, waveforms, and pitch measurements, in order to provide an objective basis for the detailed description of phonetic features of consonants, vowels, and tones. The description includes phonetic and phonological topics, involving consonants, vowels, and tones, and in addition, it deals with relevant morphological phenomena, such as the compound verb, verbal reduplication and verbal suffixes. This research also explores some theoretical issues, such as the unitary nature of clicks and their accompaniments, the integration of the clicks and non-clicks within a single set of features, the correct interpretation of tonal structure. Two types of historical sound shifts are also dealt with: namely, palatalization which is involved in the nonclick consonant system, and the click replacement which is involved in the click consonant system. In addition to the phonetic and phonological topics, selected aspects of the sociolinguistic profile of this endangered language are also documented