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TAKEUTI/ZARING. Introduction to 34 SPITZER. Principles of Random Walk. Axiomatic Set Theory. 2nd ed. 2nd ed. 2 OXTOBY. Measure and Category. 2nd ed. 35 ALEXANDER/WERMER. Several Complex 3 SCHAEFER. Topological Vector Spaces. Variables and Banach Algebras. 3rd ed. 2nd ed. 36 KELLEy/NAMIOKA et al. Linear 4 HILTON/STAMMBACH. A Course in Topological Spaces. Homological Algebra. 2nd ed. 37 MONK. Mathematical Logic. 5 MAC LANE. Categories for the Working 38 GRAUERT/FRlTZSCHE. Several Complex Mathematician. 2nd ed. Variables. 6 HUGHES/PIPER. Projective Planes. 39 ARVESON. An Invitation to C*-Algebras. 7 J.-P. SERRE. A Course in Arithmetic. 40 KEMENy/SNELUKNAPP. Denumerable 8 T AKEUn/ZARING. Axiomatic Set Theory. Markov Chains. 2nd ed. 9 HUMPHREYS. Introduction to Lie Algebras 41 ApOSTOL. Modular Functions and and Representation Theory. Dirichlet Series in Number Theory. COHEN. A Course in Simple Homotopy 2nd ed. Theory. 42 J.-P. SERRE. Linear Representations of II CONWAY. Functions of One Complex Finite Groups. Variable I. 2nd ed. 43 GILLMAN/JERlSON. Rings of Continuous BEALS. Advanced Mathematical Analysis. Functions. ANDERSON/FuLLER. Rings and Categories 44 KENDIG. Elementary Algebraic Geometry. of Modules. 2nd ed. 45 LoEVE. Probability Theory I. 4th ed. GOLUBITSKY/GUILLEMIN. Stable Mappings 46 LoEVE. Probability Theory II. 4th ed. and Their Singularities. 47 MOISE. Geometric Topology in BERBERlAN. Lectures in Functional Dimensions 2 and 3. Analysis and Operator Theory. 48 SACHS/WU. General Relativity for WINTER. The Structure of Fields. Mathematicians. ROSENBLATT. Random Processes. 2nd ed. 49 GRUENBERG/WEIR. Linear Geometry. HALMOS. Measure Theory. 2nd ed. HALMos. A Hilbert Space Problem Book. 50 EDWARDS. Fermat's Last Theorem. 2nd ed. 51 KLINGENBERG. A Course in Differential HUSEMOLLER. Fibre Bundles. 3rd ed. Geometry. HUMPHREYS. Linear Algebraic Groups. 52 HARTSHORNE. Algebraic Geometry. BARNES/MACK. An Algebraic Introduction 53 MANIN. A Course in Mathematical Logic. to Mathematical Logic. 54 GRAVER/WATKINS. Combinatorics with GREUB. Linear Algebra. 4th ed. Emphasis on the Theory of Graphs. HOLMES. Geometric Functional Analysis 55 BROWN/PEARCY. Introduction to Operator and Its Applications.

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Abstract. Let K be a connected Lie group of compact type and let T * (K) be its cotangent bundle. This paper considers geometric quantization of T * (K), first using the vertical polarization and then using a natural Kähler polarization obtained by identifying T * (K) with the complexified group K C . The first main result is that the Hilbert space obtained by using the Kähler polarization is naturally identifiable with the generalized Segal-Bargmann space introduced by the author from a different point of view, namely that of heat kernels. The second main result is that the pairing map of geometric quantization coincides with the generalized Segal-Bargmann transform introduced by the author. This means that the pairing map, in this case, is a constant multiple of a unitary map. For both results it is essential that the half-form correction be included when using the Kähler polarization.These results should be understood in the context of results of K. Wren and of the author with B. Driver concerning the quantization of (1+1)-dimensional Yang-Mills theory. Together with those results the present paper may be seen as an instance of "quantization commuting with reduction."