### Table 4 summarizes the irreducible, admissible, in nite-dimensional representations of the group PGL(2; F).

1998

"... In PAGE 8: ... Table4 : p-adic representations of PGL(2) 3 Automorphic representations of GJ and of Mp As a rst step towards the desired lift from the Jacobi group to PGL(2) we shall show in this section that the fundamental correspondence J = m SW ~ between representations of GJ and of Mp is in... ..."

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### Table 1. Dynkin diagrams corresponding to nite dimensional complex simple Lie algebras

"... In PAGE 27: ... Finite dimensional complex simple Lie algebras (2.1) Dynkin diagrams and Cartan matrices A Dynkin diagram is one of the graphs in Table1 . A Cartan matrix is one of the matrices in Table 2.... ..."

### Table 2. Cartan matrices corresponding to nite dimensional complex simple Lie algebras

### Table 1: common Euclidean and fractal objects and their fractal dimension. is true in general. For another example, consider a small number, n, of points distributed in space|for all d smaller than the minimum separation between the points the number of discs needed is precisely the same as the number of points in the set. Thus N = n d0, and the 0 exponent matches the zero-dimensionality of a point or a nite number of points. For the geometric objects introduced earlier, the relation between N and d involves a fractional exponent D: N / d?D: (1) It is only reasonable for us to say that the dimensionality of such an object is the fraction D.

### Table 1 Finite-dimensional Lie algebras of vector fields in C2 Generators Structure Label 1. f@xg C E

1994

"... In PAGE 9: ... Tables 1 { 3 at the end of the paper summarize our classi cation results for nite-dimensional Lie algebras of di eren- tial operators in two complex variables, [10], [12]. Lie apos;s classi cation of nonsingular nite-dimensional Lie algebras of vector elds on C2 is summarized in Table1 . The rst column exhibits a basis of the algebra, and the second indicates its structure as an abstract Lie algebra.... ..."

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### Table 1 Finite-dimensional Lie algebras of vector fields in C 2

1994

"... In PAGE 9: ... Tables 1 { 3 at the end of the paper summarize our classi cation results for nite-dimensional Lie algebras of di eren- tial operators in two complex variables, [10], [12]. Lie apos;s classi cation of nonsingular nite-dimensional Lie algebras of vector elds on C 2 is summarized in Table1 . The rst column exhibits a basis of the algebra, and the second indicates its structure as an abstract Lie algebra.... ..."

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### Table 2 shows the results of applying the stability tests from Theorems 2, 3, 4 (using a nite series expansion of the multiplier), and the o -axis circle criterion, for various values of H1 = L in the observer-based anti-windup scheme. The corresponding multipliers X ? W (s)

1995

"... In PAGE 23: ... Table2 : Application of various AWBT stability conditions establishing stability for the four cases above, using Theorem 4 and the nite dimensional approximation of the multiplier, as discussed in x3.2.... ..."

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### Table 2 Finite-dimensional modules for Lie algebras of vector fields Monomials? Generators Rules 1. No xie xg(y) (i; ; g) ?! (i ? 1; ; g);

1994

"... In PAGE 10: ... OLVER systems than Lie.) Table2 describes the di erent nite-dimensional modules for each of these Lie algebras. The rst column tells whether the module is necessarily spanned by monomials, i.... In PAGE 10: ... Finally, Table 4 describes the quantization condition resulting from the quasi-exactly solvability assumption that, assuming M = f1g, the Lie algebra admit a nite-dimensional module N. If the cohomol- ogy is trivial, so g is spanned by vector elds and the constant functions, then it automatically satis es the quasi-exactly solvable condition, with the associated nite-dimensional modules being explicitly described in Table2 . The maximal al- gebras, namely Case 11, sl(2) sl(2), Case 15, sl(3), and Case 24, gl(2) n Rr, play an important role in Turbiner apos;s theory of di erential equations in two dimensions with orthogonal polynomial solutions, [32].... ..."

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### Table 2 Finite-dimensional modules for Lie algebras of vector fields

1994

"... In PAGE 10: ... OLVER systems than Lie.) Table2 describes the di erent nite-dimensional modules for each of these Lie algebras. The rst column tells whether the module is necessarily spanned by monomials, i.... In PAGE 10: ... Finally, Table 4 describes the quantization condition resulting from the quasi- exactly solvability assumption that, assuming M = f1g, the Lie algebra admit a nite-dimensional module N. If the cohomol- ogy is trivial, so g is spanned by vector elds and the constant functions, then it automatically satis es the quasi-exactly solvable condition, with the associated nite-dimensional modules being explicitly described in Table2 . The maximal al- gebras, namely Case 11, sl(2) sl(2), Case 15, sl(3), and Case 24, gl(2) n Rr, play an important role in Turbiner apos;s theory of di erential equations in two dimensions with orthogonal polynomial solutions, [33].... ..."

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### Table 4 Quasi-exactly solvable Lie algebras of differential operators Quantization condition Module 1. 0

1994

"... In PAGE 10: ...ctually modi ed are indicated, i.e., those for which a = hF ; vai 6 0, cf. (17). In Case 4, Div M = ffx + gy j f; g 2 Mg. Finally, Table4 describes the quantization condition resulting from the quasi-exactly solvability assumption that, assuming M = f1g, the Lie algebra admit a nite-dimensional module N. If the cohomol- ogy is trivial, so g is spanned by vector elds and the constant functions, then it automatically satis es the quasi-exactly solvable condition, with the associated nite-dimensional modules being explicitly described in Table 2.... ..."

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