%PDF-1.5 % 4 0 obj << /S /GoTo /D (section.1) >> endobj 7 0 obj (1 Introduction) endobj 8 0 obj << /S /GoTo /D (section.2) >> endobj 11 0 obj (2 Preliminaries) endobj 12 0 obj << /S /GoTo /D (subsection.2.1) >> endobj 15 0 obj (2.1 Spherical functions) endobj 16 0 obj << /S /GoTo /D (subsection.2.2) >> endobj 19 0 obj (2.2 Root space structure of so\(n,C\)) endobj 20 0 obj << /S /GoTo /D (subsection.2.3) >> endobj 23 0 obj (2.3 The operator Q2) endobj 24 0 obj << /S /GoTo /D (subsection.2.4) >> endobj 27 0 obj (2.4 The operator Q2+1) endobj 28 0 obj << /S /GoTo /D (subsection.2.5) >> endobj 31 0 obj (2.5 Gel'fand\205Tsetlin basis) endobj 32 0 obj << /S /GoTo /D (subsection.2.6) >> endobj 35 0 obj (2.6 An explicit expression for \(Qn\)) endobj 36 0 obj << /S /GoTo /D (section.3) >> endobj 39 0 obj (3 The differential operator ) endobj 40 0 obj << /S /GoTo /D (section.4) >> endobj 43 0 obj (4 The K-types which are M-irreducible) endobj 44 0 obj << /S /GoTo /D (section.5) >> endobj 47 0 obj (5 The operator \040for fundamental K-types) endobj 48 0 obj << /S /GoTo /D (subsection.5.1) >> endobj 51 0 obj (5.1 The even case: K=SO\(2\)) endobj 52 0 obj << /S /GoTo /D (subsection.5.2) >> endobj 55 0 obj (5.2 The odd case: K=SO\(2+1\)) endobj 56 0 obj << /S /GoTo /D (section.6) >> endobj 59 0 obj (6 The spherical functions of fundamental K-types) endobj 60 0 obj << /S /GoTo /D (subsection.6.1) >> endobj 63 0 obj (6.1 -eigenvalues of spherical functions) endobj 64 0 obj << /S /GoTo /D (subsection.6.2) >> endobj 67 0 obj (6.2 Polynomial eigenfunctions of the hypergeometric operator D) endobj 68 0 obj << /S /GoTo /D (section.7) >> endobj 71 0 obj (7 The inner product) endobj 72 0 obj << /S /GoTo /D (subsection.7.1) >> endobj 75 0 obj (7.1 Spherical functions as polynomial solutions of DP=P ) endobj 76 0 obj << /S /GoTo /D (section.8) >> endobj 79 0 obj (8 Matrix valued orthogonal polynomials) endobj 80 0 obj << /S /GoTo /D (subsection.8.1) >> endobj 83 0 obj (8.1 Matrix valued orthogonal polynomials) endobj 84 0 obj << /S /GoTo /D (section.9) >> endobj 87 0 obj (9 The SO\(2+1\)-type with highest weight 2) endobj 88 0 obj << /S /GoTo /D (subsection.9.1) >> endobj 91 0 obj (9.1 Spherical functions of SO\(2+1\)-type 2) endobj 92 0 obj << /S /GoTo /D (subsection.9.2) >> endobj 95 0 obj (9.2 Matrix-valued orthogonal polynomials of size 3) endobj 96 0 obj << /S /GoTo /D (app.1) >> endobj 99 0 obj (Appendix) endobj 100 0 obj << /S /GoTo /D (ref.1) >> endobj 103 0 obj (References) endobj 104 0 obj << /S /GoTo /D [105 0 R /Fit] >> endobj 125 0 obj << /Length 3775 /Filter /FlateDecode >> stream xڝZK۸W2 .We'cǻ[*=p$Jb, Iy<{oO? Pc;o4hE'7OfYz&0jf PS~/~&| 4m+̂{nΫdpU4|c+m=_UH\rwe]AI8p}r-hSq$ʉ,1>BI*ݐߣ8qd==䛢d4&"*BB07ۢw0ycz=Z+t0QQdv(fR!\ ۈibe&B"̀'4mk,X1]weR-(F跫&)4_Mvu`!12Al)3,LWxs+\&nc8j~O}pE כ*_4?c}|#UjdhɆT9W 5C#U4Bջ1Ao*M[rKHsZvfUtMQue[}E@cP"bg8tg֠bcՓSƫ,u>]I>_ ![p "Ʈ&]jiʼx<]\Kte|$3hۮ;<{.(!*Ŋ$ U"M/ġf5#=}H~FG&,K|A-ybY_2 H~=6܂-U Wꂇ7&B uқcUX~_*]醿952s7{"r[2S jLw˅`hOxRg .UpJXm&_va/X;-l$,O/$1vٔ<-M,ow=lhx@ JK,!qzXEKs#oӿhl⑥gU;\ޞKL4L3pf=æC^6܄p,zg@W ="1[*<@*p_Xd'e]_8m3A6,j:Բ&1QPqW4{{5iwM۶6^Xגp~b,JWsХBG}ˆw6V,p&q6\]cOa"9Jo$0.6;7*swb nySp_Q-k [f[w<;T lv/wJ|X"F=%Ih Zwev&I} ܍uzw_2ߵhlޖ
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